Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-11T23:07:05.687643Z
Paper Citation Record · LEDGER
Schubert polynomials and patterns in permutations
As of 16 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.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-15T17:44:04.608797Z
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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+00:00.