Paper Citation Record · LEDGER

Richardson tableaux and components of Springer fibers equal to Richardson varieties

As of 9 August 2026, this Paper Citation Record lists 57 of 57 outbound references and 4 inbound Pith citation observations for arXiv:2506.20792.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2506.20792 v1

Coverage vector

measured 57 of 57 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T22:48:34.671953Z

measured 61 of 61 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00

measured 4 of 4 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-04T10:03:08.056396Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-07-02T19:27:19.289496Z

Reference resolution

57 of 57 outbound references displayed

verified exact2
verified fuzzy24
unresolved29
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External citation measurements

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Outbound references

Observation 5a3428fe-deb5-4d35-bf87-3da839cf782d · outbound

This paper cites Consequences of the L akshmibai-- S andhya theorem: the ubiquity of permutation patterns in S chubert calculus and related geometry.

Richardson tableaux and components of Springer fibers equal to Richardson varieties Consequences of the L akshmibai-- S andhya theorem: the ubiquity of permutation patterns in S chubert calculus and related geometry

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:43.124894Z

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Observation 573df470-d61c-403f-beaa-724a7a8ef5fe · outbound

This paper cites Combinatorics of C oxeter groups , volume 231 of Graduate Texts in Mathematics.

Richardson tableaux and components of Springer fibers equal to Richardson varieties Combinatorics of C oxeter groups , volume 231 of Graduate Texts in Mathematics

Reference 2

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Observation d0964f8f-07d2-4182-8ccf-f68c320bebc3 · outbound

This paper cites Singularities of generalized R ichardson varieties.

Richardson tableaux and components of Springer fibers equal to Richardson varieties Singularities of generalized R ichardson varieties

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:42.839314Z

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Observation aa89457c-7ac2-4574-99af-968f01e9c619 · outbound

This paper cites Acyclic matchings on Bruhat intervals and applications to total positivity.

Richardson tableaux and components of Springer fibers equal to Richardson varieties Acyclic matchings on Bruhat intervals and applications to total positivity

Reference 4

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Observation 22f6ec50-03e6-4096-94e3-665b934e8793 · outbound

This paper cites Bloch and Steven N.

Richardson tableaux and components of Springer fibers equal to Richardson varieties Bloch and Steven N

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-06T22:48:28.582001Z

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Observation 0534a24a-360a-4cbc-b5a6-126d459e1e5c · outbound

This paper cites Lakshmibai.

Richardson tableaux and components of Springer fibers equal to Richardson varieties Lakshmibai

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:42.552324Z

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Observation a942157a-421d-4d3f-a5e3-9afccd9d0c66 · outbound

This paper cites Billey and Gregory S.

Richardson tableaux and components of Springer fibers equal to Richardson varieties Billey and Gregory S

Reference 7

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Observation 8729c872-c280-4d6c-bb02-4fa67e8d1556 · outbound

This paper cites Billey and Jordan E.

Richardson tableaux and components of Springer fibers equal to Richardson varieties Billey and Jordan E

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:42.329458Z

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Observation 78bd25cc-a9ea-4e33-b63a-3a987e067da0 · outbound

This paper cites Barchini and R.

Richardson tableaux and components of Springer fibers equal to Richardson varieties Barchini and R

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:42.104140Z

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Observation 7d4261b6-c222-4175-be7d-f89a338f70f6 · outbound

This paper cites Chowla, I.

Richardson tableaux and components of Springer fibers equal to Richardson varieties Chowla, I

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:41.869714Z

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Observation 7d707d99-c21b-4560-a1e6-7a7823fbfd55 · outbound

This paper cites Singularit\'es g\'en\'eriques et quasi-r\'esolutions des vari\'et\'es de S chubert pour le groupe lin\'eaire.

Richardson tableaux and components of Springer fibers equal to Richardson varieties Singularit\'es g\'en\'eriques et quasi-r\'esolutions des vari\'et\'es de S chubert pour le groupe lin\'eaire

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:41.681781Z

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Observation cb126b8f-d42c-43d2-99b6-8dcb16575e00 · outbound

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Richardson tableaux and components of Springer fibers equal to Richardson varieties Unresolved cited work

Reference 12

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Observation 4477ede2-9edc-4133-865b-7beb4e3f4bd1 · outbound

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Richardson tableaux and components of Springer fibers equal to Richardson varieties Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:48:41.115505Z

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Richardson tableaux and components of Springer fibers equal to Richardson varieties Unresolved cited work

Reference 14

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Observation c0d0baba-f109-4dce-bb1d-6b01df728efc · outbound

This paper cites On the singularity of the irreducible components of a S pringer fiber in sl _n.

Richardson tableaux and components of Springer fibers equal to Richardson varieties On the singularity of the irreducible components of a S pringer fiber in sl _n

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:40.660244Z

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Observation 783a3b53-b025-413f-aea8-f952d18a4625 · outbound

This paper cites Some characterizations of singular components of S pringer fibers in the two-column case.

Richardson tableaux and components of Springer fibers equal to Richardson varieties Some characterizations of singular components of S pringer fibers in the two-column case

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:40.442261Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 078ee714-33a9-4246-9f40-16dead9ba854 · outbound

This paper cites On the singularity of some special components of S pringer fibers.

Richardson tableaux and components of Springer fibers equal to Richardson varieties On the singularity of some special components of S pringer fibers

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:40.220528Z

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Observation 7893bef4-3075-4428-acac-4b4c0e2a8792 · outbound

This paper cites Analytic combinatorics.

Richardson tableaux and components of Springer fibers equal to Richardson varieties Analytic combinatorics

Reference 18

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Source-reported events for the cited work

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Observation c2df85d5-19ec-48a7-b339-0f67c55eeada · outbound

This paper cites Young tableaux , volume 35 of London Mathematical Society Student Texts.

Richardson tableaux and components of Springer fibers equal to Richardson varieties Young tableaux , volume 35 of London Mathematical Society Student Texts

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:40.039151Z

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Observation af1df52a-56e2-4572-a770-b4c20b467a90 · outbound

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Richardson tableaux and components of Springer fibers equal to Richardson varieties Unresolved cited work

Reference 20

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Observation 743b194f-ac07-48e8-9b29-363365d18d25 · outbound

This paper cites Sufficiency of L akshmibai-- S andhya singularity conditions for S chubert varieties.

Richardson tableaux and components of Springer fibers equal to Richardson varieties Sufficiency of L akshmibai-- S andhya singularity conditions for S chubert varieties

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:39.696525Z

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Observation 65492485-c30f-44b5-a13f-00776b0d1b49 · outbound

This paper cites Karp, and Thomas Lam.

Richardson tableaux and components of Springer fibers equal to Richardson varieties Karp, and Thomas Lam

Reference 22

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Observation 7b3a4d7b-271d-4274-a7d6-4d190638a548 · outbound

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Richardson tableaux and components of Springer fibers equal to Richardson varieties Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:48:39.509451Z

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Observation ca6a57ff-be0c-4d29-a31a-146ddb46d14f · outbound

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Richardson tableaux and components of Springer fibers equal to Richardson varieties Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:48:39.357677Z

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Observation f09ec878-011d-4c7f-bc3d-dd063ac9a528 · outbound

This paper cites Humphreys.

Richardson tableaux and components of Springer fibers equal to Richardson varieties Humphreys

Reference 25

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Observation fba69777-24f8-4b62-acb0-459b4d9170a0 · outbound

This paper cites Nilpotent orbits in representation theory.

Richardson tableaux and components of Springer fibers equal to Richardson varieties Nilpotent orbits in representation theory

Reference 26

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Observation 4c298ecb-f7d3-49ea-8d38-cf0e2991eb3e · outbound

This paper cites Representations of C oxeter groups and H ecke algebras.

Richardson tableaux and components of Springer fibers equal to Richardson varieties Representations of C oxeter groups and H ecke algebras

Reference 27

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Observation 44e4ea2b-c921-4ac2-9295-88d3eb06196d · outbound

This paper cites The singular locus of a S chubert variety.

Richardson tableaux and components of Springer fibers equal to Richardson varieties The singular locus of a S chubert variety

Reference 28

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Observation 5ddc1b16-3b5e-43ed-93dd-ff3cd1e7ee4a · outbound

This paper cites q-Whittaker functions, finite fields, and Jordan forms.

Richardson tableaux and components of Springer fibers equal to Richardson varieties q-Whittaker functions, finite fields, and Jordan forms

Reference 29

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Observation 666579af-7aae-4ebc-bf10-ec8416ce0107 · outbound

This paper cites Kac-- M oody groups, their flag varieties and representation theory , volume 204 of Progress in Mathematics.

Richardson tableaux and components of Springer fibers equal to Richardson varieties Kac-- M oody groups, their flag varieties and representation theory , volume 204 of Progress in Mathematics

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:39.004917Z

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Observation d4c75828-9a53-4d4a-8aa1-bcac7abdbb44 · outbound

This paper cites Singularities of R ichardson varieties.

Richardson tableaux and components of Springer fibers equal to Richardson varieties Singularities of R ichardson varieties

Reference 31

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Observation f47c5a91-41f8-4960-9d23-234bd1faf9a5 · outbound

This paper cites Lakshmibai and B.

Richardson tableaux and components of Springer fibers equal to Richardson varieties Lakshmibai and B

Reference 32

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Richardson tableaux and components of Springer fibers equal to Richardson varieties Unresolved cited work

Reference 33

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Richardson tableaux and components of Springer fibers equal to Richardson varieties Unresolved cited work

Reference 34

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Richardson tableaux and components of Springer fibers equal to Richardson varieties Unresolved cited work

Reference 35

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:48:38.638362Z

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Observation 4e507a3d-cfbd-468c-97c6-e55cc194287d · outbound

This paper cites Symmetric functions, S chubert polynomials and degeneracy loci , volume 6 of SMF/AMS Texts and Monographs.

Richardson tableaux and components of Springer fibers equal to Richardson varieties Symmetric functions, S chubert polynomials and degeneracy loci , volume 6 of SMF/AMS Texts and Monographs

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:38.430420Z

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Observation 3a7b6521-e777-45c0-8e42-8c79dd199a28 · outbound

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Richardson tableaux and components of Springer fibers equal to Richardson varieties Unresolved cited work

Reference 37

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Observation f2645adc-91c3-49a5-8568-fccf7e961439 · outbound

This paper cites Etude des orbites nilpotentes par l'application de Springer g\' e n\' e ralis\' e e.

Richardson tableaux and components of Springer fibers equal to Richardson varieties Etude des orbites nilpotentes par l'application de Springer g\' e n\' e ralis\' e e

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:38.249446Z

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Observation 084be1b9-d5b3-4949-adcd-be2dbcf22cf5 · outbound

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Richardson tableaux and components of Springer fibers equal to Richardson varieties Unresolved cited work

Reference 39

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:48:38.013794Z

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Observation 5e3ecdfc-b30f-4e78-b20a-0345c51993d2 · outbound

This paper cites An algebraic cell decomposition of the nonnegative part of a flag variety.

Richardson tableaux and components of Springer fibers equal to Richardson varieties An algebraic cell decomposition of the nonnegative part of a flag variety

Reference 40

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Observation 93dcc92d-6fcc-484a-891f-0e57d719956a · outbound

This paper cites Nil-Hecke rings and the Schubert calculus.

Richardson tableaux and components of Springer fibers equal to Richardson varieties Nil-Hecke rings and the Schubert calculus

Reference 41

Resolution: verified exact; local_arxiv, observed 2026-08-06T22:48:34.892382Z

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Observation 559e1b51-c660-451a-b8df-ef1ef828170d · outbound

This paper cites S ageMath, the S age M athematics S oftware S ystem ( V ersion 10.6) , 2025.

Richardson tableaux and components of Springer fibers equal to Richardson varieties S ageMath, the S age M athematics S oftware S ystem ( V ersion 10.6) , 2025

Reference 42

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Observation 7e082d7e-a4ca-496b-aa38-446fb76e36e3 · outbound

This paper cites Spaltenstein.

Richardson tableaux and components of Springer fibers equal to Richardson varieties Spaltenstein

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:37.513407Z

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Observation c8152f72-8887-43a2-9f97-ccb3194d521d · outbound

This paper cites Classes unipotentes et sous-groupes de B orel , volume 946 of Lecture Notes in Mathematics.

Richardson tableaux and components of Springer fibers equal to Richardson varieties Classes unipotentes et sous-groupes de B orel , volume 946 of Lecture Notes in Mathematics

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:37.292010Z

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Observation 721a0562-f965-4f0c-b45d-48275ee8dec1 · outbound

This paper cites Richardson varieties, projected Richardson varieties and positroid varieties.

Richardson tableaux and components of Springer fibers equal to Richardson varieties Richardson varieties, projected Richardson varieties and positroid varieties

Reference 45

Resolution: unresolved; no resolver link, observed 2026-08-06T22:48:33.600507Z

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Observation 9d7c02dd-3569-4319-bc5d-d8c757803785 · outbound

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Richardson tableaux and components of Springer fibers equal to Richardson varieties Unresolved cited work

Reference 46

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:48:37.113705Z

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Observation 60afc7a4-4781-4754-802a-b2371de5f1e7 · outbound

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Richardson tableaux and components of Springer fibers equal to Richardson varieties Unresolved cited work

Reference 47

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:48:36.925574Z

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Observation 509a5790-c83a-4335-b69d-e388ef1f910c · outbound

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Richardson tableaux and components of Springer fibers equal to Richardson varieties Unresolved cited work

Reference 48

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:48:36.749887Z

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Observation daa5af96-7444-47f7-a9a5-7d5ec074a525 · outbound

This paper cites Richardson tableaux and S chubert positivity.

Richardson tableaux and components of Springer fibers equal to Richardson varieties Richardson tableaux and S chubert positivity

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:36.573049Z

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Observation f4fe430b-899e-4056-a574-9585cfed9e0d · outbound

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Richardson tableaux and components of Springer fibers equal to Richardson varieties Unresolved cited work

Reference 50

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Observation fd167942-a03d-4db2-bdab-11e433788d01 · outbound

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Richardson tableaux and components of Springer fibers equal to Richardson varieties Unresolved cited work

Reference 51

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:48:36.411206Z

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Observation cda472de-882b-4c13-b54d-41b93a1c5365 · outbound

This paper cites On the desingularization of the unipotent variety.

Richardson tableaux and components of Springer fibers equal to Richardson varieties On the desingularization of the unipotent variety

Reference 52

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:36.261335Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 81740a81-9cbf-46e7-b155-cd2a336eeed9 · outbound

This paper cites An occurrence of the R obinson-- S chensted correspondence.

Richardson tableaux and components of Springer fibers equal to Richardson varieties An occurrence of the R obinson-- S chensted correspondence

Reference 53

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:36.073356Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 4ec4c523-42e3-4e2c-a844-69a06b9db258 · outbound

This paper cites Orthogonal polynomials, lattice paths, and skew Y oung tableaux.

Richardson tableaux and components of Springer fibers equal to Richardson varieties Orthogonal polynomials, lattice paths, and skew Y oung tableaux

Reference 54

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:35.895539Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d94d14d8-a2d3-4137-9eb8-f58735d2c63e · outbound

This paper cites The geometry and combinatorics of S pringer fibers.

Richardson tableaux and components of Springer fibers equal to Richardson varieties The geometry and combinatorics of S pringer fibers

Reference 55

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:48:35.704472Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation c4285670-87f7-4818-a48e-03f65e812812 · outbound

This paper cites an unresolved cited work.

Richardson tableaux and components of Springer fibers equal to Richardson varieties Unresolved cited work

Reference 56

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:48:35.556844Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation f18101dd-3d67-4121-a75f-5beee0985ec5 · outbound

This paper cites an unresolved cited work.

Richardson tableaux and components of Springer fibers equal to Richardson varieties Unresolved cited work

Reference 57

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:48:35.360037Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Pith citing papers

Observation d39c6c7e-c8af-43d1-baec-66d98060a146 · inbound

Richardson tableaux and Schubert positivity cites this paper.

Richardson tableaux and Schubert positivity Richardson tableaux and components of Springer fibers equal to Richardson varieties

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-04T10:03:08.056396Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 38e34140-e344-4821-9e4d-bf08b85d6504 · inbound

Totally nonnegative maximal tori and opposed Bruhat intervals cites this paper.

Totally nonnegative maximal tori and opposed Bruhat intervals Richardson tableaux and components of Springer fibers equal to Richardson varieties

Reference 26

Resolution: verified exact; arxiv_id, observed 2026-05-13T18:03:04.588991Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 0ac31306-cb81-470b-a15f-8f1bc94e3cef · inbound

Ideals defining components of two-row Springer fibers cites this paper.

Ideals defining components of two-row Springer fibers Richardson tableaux and components of Springer fibers equal to Richardson varieties

Reference 16

Resolution: verified exact; arxiv_id, observed 2026-07-02T19:27:19.290770Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation aaf44fef-48da-43bb-821a-eb1e6202df8f · inbound

The Springer Geometry of Specht Polynomials and Schubert cycle positivity for two row Springer fiber components cites this paper.

The Springer Geometry of Specht Polynomials and Schubert cycle positivity for two row Springer fiber components Richardson tableaux and components of Springer fibers equal to Richardson varieties

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-01T18:01:24.046372Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.