Paper Citation Record · LEDGER

Commutation classes of reduced words and higher Bruhat orders for affine permutations

As of 4 August 2026, this Paper Citation Record lists 16 of 16 outbound references and 1 inbound Pith citation observation for arXiv:2604.24573.

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

pith.paper-citation-record.v1
2604.24573 v1

Coverage vector

measured 16 of 16 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-08T02:26:35.622459Z

measured 17 of 17 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-04T06:34:03.388597+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-13T05:42:29.726060Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

16 of 16 outbound references displayed

verified exact1
verified fuzzy15
unresolved0
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 91a4f494-40f1-47b9-92da-d4a4d522bb99 · outbound

This paper cites An inversion statistic for reduced words.

Commutation classes of reduced words and higher Bruhat orders for affine permutations An inversion statistic for reduced words

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T23:03:12.520884Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation f28e0897-3d52-4181-8862-09f8589fcaef · outbound

This paper cites Combinatorial descriptions of biclosed sets in affine type.

Commutation classes of reduced words and higher Bruhat orders for affine permutations Combinatorial descriptions of biclosed sets in affine type

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T23:03:12.464866Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 122abf65-1f34-47e2-a390-1d2278df0f29 · outbound

This paper cites Björner and F.

Commutation classes of reduced words and higher Bruhat orders for affine permutations Björner and F

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T23:03:12.493464Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 0c190f11-6ece-4bac-82f3-f0acf375b3e3 · outbound

This paper cites Higher Bruhat orders of types B and C.

Commutation classes of reduced words and higher Bruhat orders for affine permutations Higher Bruhat orders of types B and C

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T23:03:12.506483Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation df303ed4-258d-4946-aac5-db57f0ad47cd · outbound

This paper cites Hecke algebras and shellings of Bruhat intervals.

Commutation classes of reduced words and higher Bruhat orders for affine permutations Hecke algebras and shellings of Bruhat intervals

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T23:03:12.513984Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 1ec28b3a-fd64-4b2b-9827-fbcd2e8b2de0 · outbound

This paper cites On the weak order of Coxeter groups.

Commutation classes of reduced words and higher Bruhat orders for affine permutations On the weak order of Coxeter groups

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T23:03:12.524204Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation d8447686-81e1-4141-b7e8-cc4a7f90022c · outbound

This paper cites Thicker Soergel calculus in typeA.

Commutation classes of reduced words and higher Bruhat orders for affine permutations Thicker Soergel calculus in typeA

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T23:03:12.490500Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 9b7e40a6-c9b2-4436-99b7-7b40fa5dd0d6 · outbound

This paper cites A diamond lemma for Hecke-type algebras.

Commutation classes of reduced words and higher Bruhat orders for affine permutations A diamond lemma for Hecke-type algebras

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T23:03:12.501592Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation c1e8df90-0d8c-4761-a4ef-3998a28745fe · outbound

This paper cites Zonotopes associated with higher Bruhat orders.

Commutation classes of reduced words and higher Bruhat orders for affine permutations Zonotopes associated with higher Bruhat orders

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T23:03:12.517487Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation ab367c52-5044-4c20-851c-6d7938ac6c52 · outbound

This paper cites Diameter of the commutation classes graph of a permutation.

Commutation classes of reduced words and higher Bruhat orders for affine permutations Diameter of the commutation classes graph of a permutation

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T23:03:12.486817Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 9e6eb4ff-60ae-4949-8c51-ebdd65c1487d · outbound

This paper cites Extending higher Bruhat orders to non-longest words in $S_n$.

Commutation classes of reduced words and higher Bruhat orders for affine permutations Extending higher Bruhat orders to non-longest words in $S_n$

Reference 11

Resolution: verified exact; arxiv_id, observed 2026-05-11T22:46:12.774501Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 351754f9-704e-4e1e-8760-79860a3bd6e4 · outbound

This paper cites Steenrod operations via higher Bruhat orders.

Commutation classes of reduced words and higher Bruhat orders for affine permutations Steenrod operations via higher Bruhat orders

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T23:03:12.497443Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 1f09356c-7cd6-4eef-9fe7-8cdcf7f17758 · outbound

This paper cites Arrangements of hyperplanes, higher braid groups and higher Bruhat orders.

Commutation classes of reduced words and higher Bruhat orders for affine permutations Arrangements of hyperplanes, higher braid groups and higher Bruhat orders

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T23:03:12.483280Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation fac5c3fa-7c3f-41a6-a5e9-fb51976a2922 · outbound

This paper cites Higher Bruhat Orders in Type B.

Commutation classes of reduced words and higher Bruhat orders for affine permutations Higher Bruhat Orders in Type B

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T23:03:12.510417Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation ed3157ed-bea0-4571-be12-4226a48fae5f · outbound

This paper cites Extension spaces of oriented matroids.

Commutation classes of reduced words and higher Bruhat orders for affine permutations Extension spaces of oriented matroids

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T23:03:12.479413Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 8cf858e4-2907-4031-a5f4-e8d612174959 · outbound

This paper cites Higher Bruhat orders and cyclic hyperplane arrangements.

Commutation classes of reduced words and higher Bruhat orders for affine permutations Higher Bruhat orders and cyclic hyperplane arrangements

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T23:03:12.468448Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Pith citing papers

Observation 6e006232-28e9-47b9-bc6f-056a1dba56e9 · inbound

A ChatGPT-assisted Triangle Characterization of Affine Permutation Inversion Graphs cites this paper.

A ChatGPT-assisted Triangle Characterization of Affine Permutation Inversion Graphs Commutation classes of reduced words and higher Bruhat orders for affine permutations

Reference 4

Resolution: unresolved; no resolver link, observed 2026-07-13T05:42:29.726060Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.