Pith. sign in

Paper Citation Record · LEDGER

Formulas for Koornwinder polynomials

As of 15 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 0 inbound Pith citation observations for arXiv:2608.02810.

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

pith.paper-citation-record.v1
2608.02810 v1

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T00:55:39.407229Z

measured 28 of 28 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

28 of 28 outbound references displayed

  • verified exact12
  • verified fuzzy6
  • unresolved7
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch3

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 3c4b224a-06f0-4bd2-a1ba-6dec4c0f122f · outbound

This paper cites Non-symmetric Macdonald polynomials and Demazure-Lusztig operators.

Formulas for Koornwinder polynomials Non-symmetric Macdonald polynomials and Demazure-Lusztig operators

Reference 1

Resolution
metadata mismatch
local_arxiv, observed 2026-08-05T00:55:41.977134Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-05T00:55:37.185896Z digest=sha256:94cac4f7b260a09d7b4920e47e51a9b5ec44d1ee6cfb6c9dbcbf12bf601c5c41

Observation 2d920fab-0267-4415-a7d4-f98246fce177 · outbound

This paper cites Bourbaki, Groupes et alg\`ebres de Lie , vol.

Formulas for Koornwinder polynomials Bourbaki, Groupes et alg\`ebres de Lie , vol

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T00:55:43.377978Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-05T00:55:37.243397Z digest=sha256:f40095244f12f4c636264cfb7e18c6f60bd000dada507966ddf1dd4f56d5dc8d

Observation 71d4ae38-52dc-429f-8af5-e6671340dcd5 · outbound

This paper cites Matrix product formula for Macdonald polynomials.

Formulas for Koornwinder polynomials Matrix product formula for Macdonald polynomials

Reference 3

Resolution
verified exact
local_arxiv, observed 2026-08-05T00:55:41.785599Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-05T00:55:37.260773Z digest=sha256:e1be9f3f3951ce9fc896c54f733806232ac046b2b8a6777f62b95a5c7fe46a5a

Observation fd7fc798-0d04-4e3d-8061-bc7af3fcae7a · outbound

This paper cites Koornwinder polynomials and the stationary multi-species asymmetric exclusion process with open boundaries.

Formulas for Koornwinder polynomials Koornwinder polynomials and the stationary multi-species asymmetric exclusion process with open boundaries

Reference 4

Resolution
verified exact
local_arxiv, observed 2026-08-05T00:55:41.625293Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-05T00:55:37.307587Z digest=sha256:aaef431a7dc8cd18c48ccb25f2630660a4e6fb1aff68f42e8ae0ae1a897b97b2

Observation ac2dbdbb-b058-4196-81e4-c6a7b41e7bc5 · outbound

This paper cites Colmenarejo, L.

Formulas for Koornwinder polynomials Colmenarejo, L

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T00:55:43.297717Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-05T00:55:37.353046Z digest=sha256:4e6125628535cacc16abc50bf66f22d1bf5cd0638ffa81e379dad00891847b4c

Observation f09945b9-f064-4743-aa97-bfcc5c6f5bbe · outbound

This paper cites an unresolved cited work.

Formulas for Koornwinder polynomials Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-08-05T00:55:43.191174Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-05T00:55:37.411484Z digest=sha256:b9b50e4eccc12813b076196d1f76405465b7fa3434070ae5408575b0bc8985f6

Observation 363b69bb-33d1-4a59-9dea-b6e7a3cdd9b0 · outbound

This paper cites an unresolved cited work.

Formulas for Koornwinder polynomials Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-05T00:55:43.104775Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-05T00:55:37.574627Z digest=sha256:acaa120ece656960ece1b647337d23ea1f203433aa05c5883beaf515344fcf67

Observation ee0b1b5e-35ec-4868-a14b-4059247fec58 · outbound

This paper cites From multiline queues to Macdonald polynomials via the exclusion process.

Formulas for Koornwinder polynomials From multiline queues to Macdonald polynomials via the exclusion process

Reference 8

Resolution
verified exact
local_arxiv, observed 2026-08-05T00:55:41.482106Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-05T00:55:37.643517Z digest=sha256:efb089ccbfa99cec5e00835d675da200e877d09023f0311a9dad5bb3de8f1b47

Observation c3e826c7-81bb-4008-9fe9-ba85460ae33f · outbound

This paper cites Rhombic staircase tableaux and Koornwinder polynomials.

Formulas for Koornwinder polynomials Rhombic staircase tableaux and Koornwinder polynomials

Reference 9

Resolution
verified exact
local_arxiv, observed 2026-08-05T00:55:41.323310Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-05T00:55:37.774041Z digest=sha256:999503fdaac8729ead708e6c5d59a814d34f15dc909114d00430cefafc89bc2c

Observation 43a4ccab-f73c-4990-b156-89d2cbfb5b70 · outbound

This paper cites Set-valued tableaux for Macdonald polynomials.

Formulas for Koornwinder polynomials Set-valued tableaux for Macdonald polynomials

Reference 10

Resolution
metadata mismatch
local_arxiv, observed 2026-08-05T00:55:41.159244Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-05T00:55:37.863754Z digest=sha256:85c057ef9592a0bb788b551da51ab7644774c397d95174d68179592ef27e9bee

Observation ebdd62ac-540a-4ca5-97c9-9567c6d6d447 · outbound

This paper cites Non symmetric Cauchy kernels for the classical Groups.

Formulas for Koornwinder polynomials Non symmetric Cauchy kernels for the classical Groups

Reference 11

Resolution
verified exact
local_arxiv, observed 2026-08-05T00:55:41.009426Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-05T00:55:37.939182Z digest=sha256:abccf2d0cbb055779c5a85642e3c4bc3f8817e126337e540b20852b0948ac496

Observation 19411335-01ae-4227-87da-dcff71838b16 · outbound

This paper cites Comparing formulas for type $GL_n$ Macdonald polynomials.

Formulas for Koornwinder polynomials Comparing formulas for type $GL_n$ Macdonald polynomials

Reference 12

Resolution
verified exact
local_arxiv, observed 2026-08-05T00:55:40.871987Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-05T00:55:38.031949Z digest=sha256:5d6a398c6063f056d439c4acce89c234f61e70db8e8e6e27377267dd58feb2ea

Observation e2e366e5-804c-4baf-b209-8bed40dc3749 · outbound

This paper cites Comparing formulas for type $GL_n$ Macdonald polynomials: Supplement.

Formulas for Koornwinder polynomials Comparing formulas for type $GL_n$ Macdonald polynomials: Supplement

Reference 13

Resolution
verified exact
local_arxiv, observed 2026-08-05T00:55:40.760996Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-05T00:55:38.166188Z digest=sha256:6b328caea3302c3bd9acf246955c213045174338d7b5c945c05ebf7d8a9ec620

Observation 99319eac-eb53-464b-b88e-075c6516d6c0 · outbound

This paper cites an unresolved cited work.

Formulas for Koornwinder polynomials Unresolved cited work

Reference 14

Resolution
verified exact
raw_fallback, observed 2026-08-05T00:55:40.617865Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-05T00:55:38.256838Z digest=sha256:506b11db1909036cc40a8872a7f7ba7ce9111cb225aaeadda0733df1b5f54bb8

Observation 512297e4-1351-44cd-95e0-a510ec7c0bec · outbound

This paper cites III, 843-872.

Formulas for Koornwinder polynomials III, 843-872

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T00:55:43.034655Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-05T00:55:38.332851Z digest=sha256:f7d268110b4ac36c8f7664945ecd8c9f6d60ef7d2ca79d5077c8a46502ae2faa

Observation 3e0feec7-a801-4017-90df-8d2270ff04ef · outbound

This paper cites Triple groups and Cherednik algebras.

Formulas for Koornwinder polynomials Triple groups and Cherednik algebras

Reference 16

Resolution
metadata mismatch
local_arxiv, observed 2026-08-05T00:55:40.374830Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-05T00:55:38.436099Z digest=sha256:6eba7f669873f202fd5e0be8c5cc5b3b46c3f74683f04d56189159f94e72d3ce

Observation b379ff18-ba53-4ee4-82a1-a776729e3b6a · outbound

This paper cites an unresolved cited work.

Formulas for Koornwinder polynomials Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-08-05T00:55:42.891224Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-05T00:55:38.513860Z digest=sha256:2fc6bb25fa5456917e7cff481871ec8662e80a42f4d2832c2bc6474ea69b04a4

Observation 89e48301-8fe2-40c0-b007-5b4e223790a7 · outbound

This paper cites On Combinatorial Formulas for Macdonald Polynomials.

Formulas for Koornwinder polynomials On Combinatorial Formulas for Macdonald Polynomials

Reference 18

Resolution
verified exact
local_arxiv, observed 2026-08-05T00:55:40.198122Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-05T00:55:38.594405Z digest=sha256:ee6543fe8fa6c7145c6d6a477dfffb8256601adeb5ec1a7b4ed8e45985682c34

Observation 8b1163d5-7547-426b-9ea8-06873093f032 · outbound

This paper cites Haglund-Haiman-Loehr Type Formulas for Hall-Littlewood Polynomials of Type B and C.

Formulas for Koornwinder polynomials Haglund-Haiman-Loehr Type Formulas for Hall-Littlewood Polynomials of Type B and C

Reference 19

Resolution
verified exact
local_arxiv, observed 2026-08-05T00:55:40.036816Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-05T00:55:38.730658Z digest=sha256:922f4fc0e40bee4728577bd75e976418333de5d74f10584717c11a8b51022e08

Observation d9bf7854-02e1-4b06-9323-f31362e05491 · outbound

This paper cites ISBN: 0-19-853489-2, MR1354144.

Formulas for Koornwinder polynomials ISBN: 0-19-853489-2, MR1354144

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T00:55:42.770315Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-05T00:55:38.798150Z digest=sha256:d4c201c76f810f7f578c2a654f4cbf82d1833f25cb25c653294e135804c26b87

Observation 78d6ff0e-d6f1-4de9-8f63-710304ce0787 · outbound

This paper cites an unresolved cited work.

Formulas for Koornwinder polynomials Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-08-05T00:55:42.625381Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-05T00:55:38.861289Z digest=sha256:400de7ca4102da141e67f9d6bd96a2af08497f89c494c5b50cbf5ce5d0cd6873

Observation ef96a4ce-9411-4831-9817-fe31fe0810cf · outbound

This paper cites 157, Cambridge University Press, Cambridge, 2003.

Formulas for Koornwinder polynomials 157, Cambridge University Press, Cambridge, 2003

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T00:55:42.531337Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-05T00:55:38.936427Z digest=sha256:0e8113a5d20b831535763ab26d708d12e9e5643ac2feb9070d4759e2ac6637f7

Observation 8669c9c1-1d92-4172-88a2-5aa902bc3439 · outbound

This paper cites an unresolved cited work.

Formulas for Koornwinder polynomials Unresolved cited work

Reference 23

Resolution
unresolved
raw_fallback, observed 2026-08-05T00:55:42.417991Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-05T00:55:39.028535Z digest=sha256:3b208def8af7040d593b72086ca68bbb70ca2e78fde0f0f68e55000492d9a844

Observation 170e96ca-b7e5-4e8e-bb1a-e5117f08791b · outbound

This paper cites A combinatorial formula for Macdonald polynomials.

Formulas for Koornwinder polynomials A combinatorial formula for Macdonald polynomials

Reference 24

Resolution
verified exact
local_arxiv, observed 2026-08-05T00:55:39.819987Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-05T00:55:39.092234Z digest=sha256:a9ded6ef2ccf25273bb48dd79d5557027dfd63334052bf4a4de5b6cbfeef6741

Observation c0380e67-a903-4e9a-9e81-687ec9f76266 · outbound

This paper cites Specializations of nonsymmetric Macdonald-Koornwinder polynomials.

Formulas for Koornwinder polynomials Specializations of nonsymmetric Macdonald-Koornwinder polynomials

Reference 25

Resolution
verified exact
local_arxiv, observed 2026-08-05T00:55:39.644747Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-05T00:55:39.184441Z digest=sha256:c855d51be1160e23062b3cd7045ecb2a3cfbd9f8cca63610201b77956562f771

Observation 41ebe9cf-dd7b-4d2e-81db-757d644b5803 · outbound

This paper cites MR1715325.

Formulas for Koornwinder polynomials MR1715325

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T00:55:42.261542Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-05T00:55:39.261278Z digest=sha256:2fc188ef45398468e7403a47cb61bdc0292d9587d80b363e744c666c267f5c0e

Observation 56c06896-aef1-43bb-96df-d250ee389ca1 · outbound

This paper cites an unresolved cited work.

Formulas for Koornwinder polynomials Unresolved cited work

Reference 27

Resolution
unresolved
raw_fallback, observed 2026-08-05T00:55:42.149405Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-05T00:55:39.360200Z digest=sha256:1f393170a7ce3f051ad9f62456ed7d7fcd8b911c9d9b6a2a5f065026da56b362

Observation e1a2a44c-a2ee-4738-bf18-f0c06d34169f · outbound

This paper cites an unresolved cited work.

Formulas for Koornwinder polynomials Unresolved cited work

Reference 28

Resolution
unresolved
raw_fallback, observed 2026-08-05T00:55:42.074864Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-05T00:55:39.407229Z digest=sha256:e5ffcc2d4b8fb1d41212a72bd31fc2ac25b753b0673e1600d1544d0f2e58b624

Pith citing papers

No inbound Pith citation observations are available.