Paper Citation Record · LEDGER

Square root crystals and the square root of $B(\infty)$

As of 22 August 2026, this Paper Citation Record lists 52 of 52 outbound references and 0 inbound Pith citation observations for arXiv:2608.11009.

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

pith.paper-citation-record.v1
2608.11009 v1

Coverage vector

measured 52 of 52 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-12T12:21:59.442115Z

measured 52 of 52 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

52 of 52 outbound references displayed

verified exact0
verified fuzzy37
unresolved15
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation a4c36545-6372-41d1-b191-8877fcf013cd · outbound

This paper cites Multiline queues with spectral parameters.

Square root crystals and the square root of $B(\infty)$ Multiline queues with spectral parameters

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:22:00.315842Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 9eaffb62-ee97-4d96-9132-fda32d55702d · outbound

This paper cites an unresolved cited work.

Square root crystals and the square root of $B(\infty)$ Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-12T12:22:00.298882Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation b59750f1-3da2-4ad7-abc6-f744eef75afc · outbound

This paper cites Crystal bases for the quantum superalgebra U_q( gl (m,n)).

Square root crystals and the square root of $B(\infty)$ Crystal bases for the quantum superalgebra U_q( gl (m,n))

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:22:00.282130Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation b1dccf90-1ea2-4310-a2f4-db0349f20a03 · outbound

This paper cites Lie groups and L ie algebras.

Square root crystals and the square root of $B(\infty)$ Lie groups and L ie algebras

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:22:00.265001Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation bbfeef3c-2356-4b42-905b-3bd74b9dfcd8 · outbound

This paper cites Crystal bases.

Square root crystals and the square root of $B(\infty)$ Crystal bases

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-12T12:21:59.191477Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b38c7e24-25fa-4208-87b5-04503ab4d264 · outbound

This paper cites Colored five-vertex models and L ascoux polynomials and atoms.

Square root crystals and the square root of $B(\infty)$ Colored five-vertex models and L ascoux polynomials and atoms

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:22:00.236414Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation a3c6375d-3c1f-4890-8ae7-1d416ded7387 · outbound

This paper cites A L ittlewood-- R ichardson rule for the K -theory of G rassmannians.

Square root crystals and the square root of $B(\infty)$ A L ittlewood-- R ichardson rule for the K -theory of G rassmannians

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:22:00.219540Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 4372ed32-8e66-4e5b-b208-b9ea52cafba4 · outbound

This paper cites String bases for quantum groups of type A_r.

Square root crystals and the square root of $B(\infty)$ String bases for quantum groups of type A_r

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:22:00.202617Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation af442e06-16dc-4502-af95-835701f2dbb1 · outbound

This paper cites Tensor product multiplicities, canonical bases and totally positive varieties.

Square root crystals and the square root of $B(\infty)$ Tensor product multiplicities, canonical bases and totally positive varieties

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:22:00.186088Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation f7aff5a1-5430-4ca0-b2af-0974396252ea · outbound

This paper cites Crystal bases and Y oung tableaux.

Square root crystals and the square root of $B(\infty)$ Crystal bases and Y oung tableaux

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:22:00.169275Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation e1ea319e-49d9-4897-940c-a8cb51dfd697 · outbound

This paper cites Representation theory , volume 129 of Graduate Texts in Mathematics.

Square root crystals and the square root of $B(\infty)$ Representation theory , volume 129 of Graduate Texts in Mathematics

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-12T12:21:59.224659Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 73a771f7-f9b5-485e-9b08-18dc84501fbf · outbound

This paper cites Kirillov.

Square root crystals and the square root of $B(\infty)$ Kirillov

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:22:00.142183Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 0567a447-f49e-4818-95df-075bb1cb0db3 · outbound

This paper cites Quantum queer superalgebra and crystal bases.

Square root crystals and the square root of $B(\infty)$ Quantum queer superalgebra and crystal bases

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:22:00.125028Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 2871d563-ab4b-4bb1-9392-643ca5c884e4 · outbound

This paper cites Crystal bases for the quantum queer superalgebra and semistandard decomposition tableaux.

Square root crystals and the square root of $B(\infty)$ Crystal bases for the quantum queer superalgebra and semistandard decomposition tableaux

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-12T12:21:59.240546Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1a52abfa-8c87-49ff-84c2-a322fa0613c0 · outbound

This paper cites Grojnowski and G.

Square root crystals and the square root of $B(\infty)$ Grojnowski and G

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:22:00.096556Z

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 674dc3c8-e7fc-40e1-a69a-77235c3b31e4 · outbound

This paper cites Introduction to quantum groups and crystal bases , volume 42 of Graduate Studies in Mathematics.

Square root crystals and the square root of $B(\infty)$ Introduction to quantum groups and crystal bases , volume 42 of Graduate Studies in Mathematics

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-12T12:21:59.251210Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fe374bed-ea4c-4118-88f1-d81bcbb40dcb · outbound

This paper cites Young tableaux and crystal B( ) for finite simple L ie algebras.

Square root crystals and the square root of $B(\infty)$ Young tableaux and crystal B( ) for finite simple L ie algebras

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:22:00.067877Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 272c769d-688b-4a73-a232-e044e51e07cc · outbound

This paper cites Humphreys.

Square root crystals and the square root of $B(\infty)$ Humphreys

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-12T12:21:59.261238Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8279d2e1-6eff-4a03-bb94-4df79ad1b48e · outbound

This paper cites Humphreys.

Square root crystals and the square root of $B(\infty)$ Humphreys

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-12T12:21:59.266524Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a25c504b-91a7-4645-981e-6e4fbf902507 · outbound

This paper cites Humphreys.

Square root crystals and the square root of $B(\infty)$ Humphreys

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:22:00.024787Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 04e50eff-9021-4762-97ac-fdd250d20123 · outbound

This paper cites Quantum groups and their primitive ideals , volume 29 of Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)].

Square root crystals and the square root of $B(\infty)$ Quantum groups and their primitive ideals , volume 29 of Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)]

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:22:00.003791Z

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 9df7b3d2-8ba7-4232-ad05-a46566415e7f · outbound

This paper cites Mirkovi\'c-- V ilonen cycles and polytopes.

Square root crystals and the square root of $B(\infty)$ Mirkovi\'c-- V ilonen cycles and polytopes

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:21:59.982681Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5e756c31-0e88-484b-9c0c-e5130543d069 · outbound

This paper cites Crystalizing the q -analogue of universal enveloping algebras.

Square root crystals and the square root of $B(\infty)$ Crystalizing the q -analogue of universal enveloping algebras

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-12T12:21:59.288738Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 946cefa6-2bc2-4230-9df9-7aa860be9d0b · outbound

This paper cites Kashiwara.

Square root crystals and the square root of $B(\infty)$ Kashiwara

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-12T12:21:59.293752Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bf5021c7-70c1-45c3-8c40-dc61bcf9c9cd · outbound

This paper cites The crystal base and L ittelmann's refined D emazure character formula.

Square root crystals and the square root of $B(\infty)$ The crystal base and L ittelmann's refined D emazure character formula

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-12T12:21:59.298834Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation accdec05-13fe-4974-8519-65682f2180d7 · outbound

This paper cites On crystal bases.

Square root crystals and the square root of $B(\infty)$ On crystal bases

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:21:59.929613Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 4ebc7fbf-8fdb-41ca-b2a9-dc07dbac8fda · outbound

This paper cites Kirillov.

Square root crystals and the square root of $B(\infty)$ Kirillov

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:21:59.912519Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 227af695-fdef-48bb-9ea7-f5d2dfacdfa6 · outbound

This paper cites Crystal graphs for representations of the q -analogue of classical L ie algebras.

Square root crystals and the square root of $B(\infty)$ Crystal graphs for representations of the q -analogue of classical L ie algebras

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:21:59.895037Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 89fcc602-ed85-43f7-befd-a33aeec8c831 · outbound

This paper cites Geometric construction of crystal bases.

Square root crystals and the square root of $B(\infty)$ Geometric construction of crystal bases

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:21:59.877613Z

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 77d6cffb-631a-4c1a-8839-1a5dd7bb14f1 · outbound

This paper cites an unresolved cited work.

Square root crystals and the square root of $B(\infty)$ Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-12T12:21:59.860132Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 0f286a04-fade-42c3-82e1-503eae26bb8a · outbound

This paper cites Combinatorial aspects of the K -theory of G rassmannians.

Square root crystals and the square root of $B(\infty)$ Combinatorial aspects of the K -theory of G rassmannians

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:21:59.842865Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation f0faf346-bb7c-4201-9c46-3ba6be7a5f9c · outbound

This paper cites On the combinatorics of crystal graphs.

Square root crystals and the square root of $B(\infty)$ On the combinatorics of crystal graphs

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:21:59.825678Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 2b08c636-e28a-4ec5-ae14-30b561bd6c26 · outbound

This paper cites Crystal graphs and Y oung tableaux.

Square root crystals and the square root of $B(\infty)$ Crystal graphs and Y oung tableaux

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:21:59.808446Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation f9a8b31a-5f95-4dbf-830a-8b89ce4907d2 · outbound

This paper cites Cones, crystals, and patterns.

Square root crystals and the square root of $B(\infty)$ Cones, crystals, and patterns

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:21:59.788358Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation bf81f5b7-0e06-403b-8e36-0de55d970840 · outbound

This paper cites Lakshmibai, C.

Square root crystals and the square root of $B(\infty)$ Lakshmibai, C

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:21:59.771422Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation e1c9ab7a-c89b-43bd-8f33-bc84bf09f995 · outbound

This paper cites Structure de H opf de l'anneau de cohomologie et de l'anneau de G rothendieck d'une vari\'et\'e de drapeaux.

Square root crystals and the square root of $B(\infty)$ Structure de H opf de l'anneau de cohomologie et de l'anneau de G rothendieck d'une vari\'et\'e de drapeaux

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:21:59.754956Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 3d28a029-660a-4d8b-97d5-b04ea30733a0 · outbound

This paper cites Symmetry and flag manifolds.

Square root crystals and the square root of $B(\infty)$ Symmetry and flag manifolds

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:21:59.738018Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5562331b-70fc-4989-9538-cce86fb4e796 · outbound

This paper cites Keys & standard bases.

Square root crystals and the square root of $B(\infty)$ Keys & standard bases

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:21:59.719670Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation a2c6dd8b-c313-46af-99c0-4f74d8b13b25 · outbound

This paper cites an unresolved cited work.

Square root crystals and the square root of $B(\infty)$ Unresolved cited work

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-12T12:21:59.373331Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d25acb0c-05e2-45db-bfa8-2d5f0f552ee6 · outbound

This paper cites an unresolved cited work.

Square root crystals and the square root of $B(\infty)$ Unresolved cited work

Reference 40

Resolution: unresolved; raw_fallback, observed 2026-08-12T12:21:59.691210Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 636fc398-b068-4b7a-bbf5-4779d3999b7e · outbound

This paper cites Introduction to quantum groups , volume 110 of Progress in Mathematics.

Square root crystals and the square root of $B(\infty)$ Introduction to quantum groups , volume 110 of Progress in Mathematics

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-12T12:21:59.384653Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b89e1bb5-8cfe-4b8b-b480-e124723748cd · outbound

This paper cites Set-Valued Skyline Fillings.

Square root crystals and the square root of $B(\infty)$ Set-Valued Skyline Fillings

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-12T12:21:59.389698Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2ad0fec7-3469-4939-bed8-6d0203c34b42 · outbound

This paper cites Crystal structures for symmetric G rothendieck polynomials.

Square root crystals and the square root of $B(\infty)$ Crystal structures for symmetric G rothendieck polynomials

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:21:59.662767Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation cd010ef6-323b-4d03-b2a9-b00ff2175254 · outbound

This paper cites Crystals for set-valued decomposition tableaux.

Square root crystals and the square root of $B(\infty)$ Crystals for set-valued decomposition tableaux

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:21:59.646381Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 988e366b-896a-4ccd-9e95-de666d7b1a8b · outbound

This paper cites Grothendieck positivity for normal square root crystals.

Square root crystals and the square root of $B(\infty)$ Grothendieck positivity for normal square root crystals

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:21:59.629683Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 160fb83f-1bbc-4e7c-8c9a-591546977655 · outbound

This paper cites Polyhedral realizations of crystal bases for integrable highest weight modules.

Square root crystals and the square root of $B(\infty)$ Polyhedral realizations of crystal bases for integrable highest weight modules

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:21:59.612857Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 12c36942-0a34-434c-bda6-d4b6893c8c88 · outbound

This paper cites Polyhedral realizations of crystal bases for quantized K ac-- M oody algebras.

Square root crystals and the square root of $B(\infty)$ Polyhedral realizations of crystal bases for quantized K ac-- M oody algebras

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:21:59.594660Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 2c1c3a43-58e5-49e1-8495-dbbfeefc6909 · outbound

This paper cites K-theoretic crystals for set-valued tableaux of rectangular shapes.

Square root crystals and the square root of $B(\infty)$ K-theoretic crystals for set-valued tableaux of rectangular shapes

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:21:59.576395Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation f5a3229a-37ba-472b-8d2c-09404944e12f · outbound

This paper cites Combinatorial rules for three bases of polynomials.

Square root crystals and the square root of $B(\infty)$ Combinatorial rules for three bases of polynomials

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:21:59.557959Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation c5300cad-7652-4647-9c18-f5d6bf3ecb9f · outbound

This paper cites Candidate for the crystal B(- ) for the queer L ie superalgebra.

Square root crystals and the square root of $B(\infty)$ Candidate for the crystal B(- ) for the queer L ie superalgebra

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:21:59.541038Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation f3240c50-894c-4396-b28b-40533be4c814 · outbound

This paper cites Grothendieck-to- L ascoux expansions.

Square root crystals and the square root of $B(\infty)$ Grothendieck-to- L ascoux expansions

Reference 51

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:21:59.523012Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 4cf632fb-7af4-407e-990b-abb06fdf2e73 · outbound

This paper cites Set-valued tableaux rule for L ascoux polynomials.

Square root crystals and the square root of $B(\infty)$ Set-valued tableaux rule for L ascoux polynomials

Reference 52

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T12:21:59.505745Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Pith citing papers

No inbound Pith citation observations are available.