Paper Citation Record · LEDGER

Schubert polynomials and patterns in permutations

As of 21 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 2 inbound Pith citation observations for arXiv:2412.02932.

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

pith.paper-citation-record.v1
2412.02932 v1

Coverage vector

measured 23 of 23 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T23:07:05.687643Z

measured 25 of 25 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T17:44:04.608797Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-10T06:15:00.866473Z

Reference resolution

23 of 23 outbound references displayed

verified exact1
verified fuzzy17
unresolved5
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 5959203c-70a8-49fa-9345-7c681274d1ef · outbound

This paper cites an unresolved cited work.

Schubert polynomials and patterns in permutations Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-11T23:07:06.521934Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 233fb87e-261c-4465-a4ec-4dc38ccdb68c · outbound

This paper cites Demazure, D´ esingularisation des vari´ et´ es de Schubert g´ en´ eralis´ ees, Ann.

Schubert polynomials and patterns in permutations Demazure, D´ esingularisation des vari´ et´ es de Schubert g´ en´ eralis´ ees, Ann

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:07:06.495837Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 09671377-150b-4699-be02-f1c83744cd96 · outbound

This paper cites Demazure, Une nouvelle formule des caract´ eres, Bull.

Schubert polynomials and patterns in permutations Demazure, Une nouvelle formule des caract´ eres, Bull

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:07:06.457325Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation cb8df8fe-a406-4813-8abd-e14368e11094 · outbound

This paper cites Pattern bounds for principal specializations of $\beta$-Grothendieck Polynomials.

Schubert polynomials and patterns in permutations Pattern bounds for principal specializations of $\beta$-Grothendieck Polynomials

Reference 4

Resolution: verified exact; local_arxiv, observed 2026-08-11T23:07:05.835853Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 0b0b6634-544e-4ef3-8e55-1fa5ba68b75f · outbound

This paper cites an unresolved cited work.

Schubert polynomials and patterns in permutations Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-11T23:07:06.426019Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation db968b7b-b939-45f0-8d90-66eafb53d6c8 · outbound

This paper cites an unresolved cited work.

Schubert polynomials and patterns in permutations Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-11T23:07:06.402289Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 3fe3c8d5-0189-4fe4-b6dd-1ea904b4441d · outbound

This paper cites Fomin and R.P.

Schubert polynomials and patterns in permutations Fomin and R.P

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:07:06.370578Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation ec85ab6c-6001-4a90-902e-afb53fe12cb7 · outbound

This paper cites Gao, Principal specializations of Schubert polynomials and patt ern containment, European J.

Schubert polynomials and patterns in permutations Gao, Principal specializations of Schubert polynomials and patt ern containment, European J

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:07:06.332179Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation eb7d97a5-480b-4da0-9ff4-42e292055026 · outbound

This paper cites Zero-one dual characters of flagged Weyl modules.

Schubert polynomials and patterns in permutations Zero-one dual characters of flagged Weyl modules

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-11T23:07:05.526200Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a87570bd-4def-429c-af6a-d7a83c149361 · outbound

This paper cites Hamaker, O.

Schubert polynomials and patterns in permutations Hamaker, O

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:07:06.295871Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 9e9492b0-09f4-4481-b10c-99c2f2790633 · outbound

This paper cites Kra´ skiewicz and P.

Schubert polynomials and patterns in permutations Kra´ skiewicz and P

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:07:06.266669Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation d18d077d-fa7a-444e-b183-f040848d95db · outbound

This paper cites Kra´ skiewicz and P.

Schubert polynomials and patterns in permutations Kra´ skiewicz and P

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:07:06.236353Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 87acca25-124f-4294-8e84-18599445da12 · outbound

This paper cites Lascoux, M.-P.

Schubert polynomials and patterns in permutations Lascoux, M.-P

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:07:06.202384Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation ec29a2f5-030a-4d6f-ba84-f6d71464b413 · outbound

This paper cites Macdonald, Notes on Schubert Polynomials, Laboratoire de combinatoire et d’informatique math´ ematique (LACIM), Universit´ e du Qu´ ebec ´ aMontr´ eal, Montreal, 1991.

Schubert polynomials and patterns in permutations Macdonald, Notes on Schubert Polynomials, Laboratoire de combinatoire et d’informatique math´ ematique (LACIM), Universit´ e du Qu´ ebec ´ aMontr´ eal, Montreal, 1991

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:07:06.174060Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation a98fe651-2298-4a82-b71a-804c93c97740 · outbound

This paper cites Magyar, Schubert polynomials and Bott–Samelson varieties, Comment.

Schubert polynomials and patterns in permutations Magyar, Schubert polynomials and Bott–Samelson varieties, Comment

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:07:06.150869Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation ab04eead-1c08-4f30-8bb3-2ae5636ccddc · outbound

This paper cites Merzon and E.

Schubert polynomials and patterns in permutations Merzon and E

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:07:06.127390Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 12b210fe-9c52-4b11-858f-67c7f387c134 · outbound

This paper cites M´ esz´ aros, A.

Schubert polynomials and patterns in permutations M´ esz´ aros, A

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:07:06.089660Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation d4654bd1-70c4-4a47-8b70-cf7c29aa6b23 · outbound

This paper cites M´ esz´ aros and A.

Schubert polynomials and patterns in permutations M´ esz´ aros and A

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:07:06.020940Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation ded0abb0-763f-461a-be4c-4bc5d7f5215b · outbound

This paper cites Monical, N.

Schubert polynomials and patterns in permutations Monical, N

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:07:05.989794Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 9f5ed759-54f7-4aef-847b-5978d38de2b5 · outbound

This paper cites Morales, I.

Schubert polynomials and patterns in permutations Morales, I

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:07:05.949327Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation e09d2415-2dac-4a0a-9309-7a593f67dfba · outbound

This paper cites Some Schubert shenanigans.

Schubert polynomials and patterns in permutations Some Schubert shenanigans

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-11T23:07:05.670421Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d383d5c0-6939-4eee-8b1f-7ca25150d51c · outbound

This paper cites Weigandt, Schubert polynomials, 132-patterns, and Stanle y’s conjecture, Algebr.

Schubert polynomials and patterns in permutations Weigandt, Schubert polynomials, 132-patterns, and Stanle y’s conjecture, Algebr

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:07:05.905862Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 4ba39664-1c3f-4b33-9915-69091a97de78 · outbound

This paper cites Zhang, Principal specializations of Schubert polynomials, mult i-layered permu- tations and asymptotics, Adv.

Schubert polynomials and patterns in permutations Zhang, Principal specializations of Schubert polynomials, mult i-layered permu- tations and asymptotics, Adv

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T23:07:05.884086Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Pith citing papers

Observation 4afb227a-ed3d-4f65-8e01-0ea66ba66e3b · inbound

Newton polytopes of fireworks Grothendieck polynomials cites this paper.

Newton polytopes of fireworks Grothendieck polynomials Schubert polynomials and patterns in permutations

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-15T17:44:04.608797Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 653b6b1f-b64a-40c4-9902-81eaa2af7ed2 · inbound

Injectivity of symmetric polynomial maps on partitions cites this paper.

Injectivity of symmetric polynomial maps on partitions Schubert polynomials and patterns in permutations

Reference 12

Resolution: verified exact; arxiv_id, observed 2026-06-26T17:29:37.996635Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.