Paper Citation Record · LEDGER

When is the chromatic quasisymmetric function symmetric?

As of 19 August 2026, this Paper Citation Record lists 39 of 39 outbound references and 1 inbound Pith citation observation for arXiv:2412.10556.

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

pith.paper-citation-record.v1
2412.10556 v2

Coverage vector

measured 39 of 39 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T16:16:24.366861Z

measured 40 of 40 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-05T15:26:41.096697Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-05T15:26:41.398188Z

Reference resolution

39 of 39 outbound references displayed

verified exact13
verified fuzzy8
unresolved12
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malformed identifier5
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External citation measurements

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Outbound references

Observation 7a8a6871-e185-49e9-a283-42687a89d150 · outbound

This paper cites Chromatic symmetric functions from the modular law.

When is the chromatic quasisymmetric function symmetric? Chromatic symmetric functions from the modular law

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-11T16:16:24.156948Z

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Observation 1ac44800-3a39-4d10-b054-6a94ad62f759 · outbound

This paper cites LLT polynomials, chromatic quasisymmetric func- tions and graphs with cycles.

When is the chromatic quasisymmetric function symmetric? LLT polynomials, chromatic quasisymmetric func- tions and graphs with cycles

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-11T16:16:24.162337Z

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Observation c250be69-b06c-446b-bbd2-f8cfbbc9f565 · outbound

This paper cites The chromatic symmetric function of a graph centred at a vertex.

When is the chromatic quasisymmetric function symmetric? The chromatic symmetric function of a graph centred at a vertex

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:16:25.353015Z

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Observation 0037e48b-74cd-48e1-b92c-c0fd29392cd0 · outbound

This paper cites Chromatic Quasisymmetric Functions of the Path Graph.

When is the chromatic quasisymmetric function symmetric? Chromatic Quasisymmetric Functions of the Path Graph

Reference 4

Resolution: verified exact; doi, observed 2026-08-11T16:16:24.619691Z

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Observation 8bcf323e-e9bb-4751-856d-a1a46167c818 · outbound

This paper cites Unit interval orders and the dot action on the cohomology of regular semisimple Hessenberg varieties.

When is the chromatic quasisymmetric function symmetric? Unit interval orders and the dot action on the cohomology of regular semisimple Hessenberg varieties

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:16:25.335854Z

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Observation 65a1e95f-dea4-443b-8aa5-4f44c381a894 · outbound

This paper cites Positivity of chromatic symmetric functions associated with Hessenberg functions of bounce number 3.

When is the chromatic quasisymmetric function symmetric? Positivity of chromatic symmetric functions associated with Hessenberg functions of bounce number 3

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:16:25.318442Z

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Observation f92d4e34-ec65-427a-82d2-7c390cdf9621 · outbound

This paper cites On e-positivity and e-unimodality of chromatic quasi-symmetric functions.

When is the chromatic quasisymmetric function symmetric? On e-positivity and e-unimodality of chromatic quasi-symmetric functions

Reference 7

Resolution: verified exact; doi, observed 2026-08-11T16:16:24.592853Z

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Observation c301b497-6070-4588-8d06-b3eb17311cef · outbound

This paper cites Chromatic symmetric func- tions of Dyck paths and q-rook theory.

When is the chromatic quasisymmetric function symmetric? Chromatic symmetric func- tions of Dyck paths and q-rook theory

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:16:25.299907Z

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Observation 8c338eaf-cc0b-4233-bc42-7752dedea2f1 · outbound

This paper cites Triangular Ladders $P_{d,2}$ are $e$-positive.

When is the chromatic quasisymmetric function symmetric? Triangular Ladders $P_{d,2}$ are $e$-positive

Reference 9

Resolution: verified exact; local_arxiv, observed 2026-08-11T16:16:25.007010Z

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Observation ea352f4f-f3d0-4eab-8a5e-c7bda4cb8be1 · outbound

This paper cites Lollipop and lariat symmetric func- tions.

When is the chromatic quasisymmetric function symmetric? Lollipop and lariat symmetric func- tions

Reference 10

Resolution: verified exact; doi, observed 2026-08-11T16:16:24.575146Z

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Observation fbf4207f-968a-4895-9e38-b391e2eaefa1 · outbound

This paper cites A decomposition theorem for partially ordered sets.

When is the chromatic quasisymmetric function symmetric? A decomposition theorem for partially ordered sets

Reference 11

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Observation 08c3f79d-b5ac-4af2-a36e-d4632cf2d930 · outbound

This paper cites A directed graph generalization of chromatic quasisymmetric functions.

When is the chromatic quasisymmetric function symmetric? A directed graph generalization of chromatic quasisymmetric functions

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-11T16:16:24.239458Z

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Observation d7f40cf6-9bb1-429b-9165-e851dba9ca38 · outbound

This paper cites On enumerators of Smirnov words by descents and cyclic descents.

When is the chromatic quasisymmetric function symmetric? On enumerators of Smirnov words by descents and cyclic descents

Reference 13

Resolution: verified exact; doi, observed 2026-08-11T16:16:24.547362Z

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Observation cde8765d-cb6d-4c60-bfbf-e69e399a0481 · outbound

This paper cites Classes of graphs withe-positive chromatic symmetric function.

When is the chromatic quasisymmetric function symmetric? Classes of graphs withe-positive chromatic symmetric function

Reference 14

Resolution: malformed identifier; no resolver link, observed 2026-08-11T16:16:24.250393Z

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Observation aec4d44c-49e9-466b-8f75-fcb5947ca488 · outbound

This paper cites Incomparability graphs of (3 + 1)-free posets are s-positive.

When is the chromatic quasisymmetric function symmetric? Incomparability graphs of (3 + 1)-free posets are s-positive

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:16:25.278621Z

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Observation 06855f40-d19a-40bf-8ae4-a37e79a82c39 · outbound

This paper cites A chromatic symmetric function in noncommuting variables.

When is the chromatic quasisymmetric function symmetric? A chromatic symmetric function in noncommuting variables

Reference 16

Resolution: verified exact; doi, observed 2026-08-11T16:16:24.516227Z

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Observation 291983d8-d231-45bf-aa66-b752f83a65e6 · outbound

This paper cites On Macdonald expansions of $q$-chromatic symmetric functions and the Stanley-Stembridge Conjecture.

When is the chromatic quasisymmetric function symmetric? On Macdonald expansions of $q$-chromatic symmetric functions and the Stanley-Stembridge Conjecture

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-11T16:16:24.264500Z

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Observation c6287a19-5e13-47fd-80f2-02eac829d96f · outbound

This paper cites Hopf Algebras in Combinatorics.

When is the chromatic quasisymmetric function symmetric? Hopf Algebras in Combinatorics

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-11T16:16:24.270849Z

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Observation 2a89d945-c746-43d5-b801-8e7d1f39c959 · outbound

This paper cites A modular relation for the chromatic symmetric functions of (3+1)-free posets.

When is the chromatic quasisymmetric function symmetric? A modular relation for the chromatic symmetric functions of (3+1)-free posets

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-11T16:16:24.276540Z

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Observation 785aed58-1933-4b4c-a0ad-11d5d3e3e326 · outbound

This paper cites A second proof of the Shareshian--Wachs conjecture, by way of a new Hopf algebra.

When is the chromatic quasisymmetric function symmetric? A second proof of the Shareshian--Wachs conjecture, by way of a new Hopf algebra

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-11T16:16:24.282460Z

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Observation e13f7616-e910-4bde-acde-7c0bb4c5e3cd · outbound

This paper cites The cohomology of abelian Hessenberg varieties and the Stanley-Stembridge conjecture.

When is the chromatic quasisymmetric function symmetric? The cohomology of abelian Hessenberg varieties and the Stanley-Stembridge conjecture

Reference 21

Resolution: verified exact; doi, observed 2026-08-11T16:16:24.497774Z

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Observation 02db554e-78b1-4aef-a395-5b7017b64505 · outbound

This paper cites Explicit polynomial generators for the ring of quasisymmetric functions over the integers.

When is the chromatic quasisymmetric function symmetric? Explicit polynomial generators for the ring of quasisymmetric functions over the integers

Reference 22

Resolution: verified exact; doi, observed 2026-08-11T16:16:24.479372Z

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Observation b2138a61-bbde-42d3-95ff-a9127fdb4c80 · outbound

This paper cites A proof of the Stanley-Stembridge conjecture.

When is the chromatic quasisymmetric function symmetric? A proof of the Stanley-Stembridge conjecture

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:16:25.257695Z

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Observation 1ae47015-9fb1-4cf4-a14b-b74a483186a8 · outbound

This paper cites Melting lollipop chromatic quasisymmetric functions and Schur expansion of unicellular LLT polynomials.

When is the chromatic quasisymmetric function symmetric? Melting lollipop chromatic quasisymmetric functions and Schur expansion of unicellular LLT polynomials

Reference 24

Resolution: metadata mismatch; raw_fallback, observed 2026-08-11T16:16:24.891567Z

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Observation a902d0b9-cca6-44b9-ab93-a92e7938921d · outbound

This paper cites P-partition products and fundamental quasi-symmetric function positivity.

When is the chromatic quasisymmetric function symmetric? P-partition products and fundamental quasi-symmetric function positivity

Reference 25

Resolution: verified exact; doi, observed 2026-08-11T16:16:24.461755Z

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Observation 848bd521-3f66-4e47-a913-51a9aad6f910 · outbound

This paper cites On the e-positivity of ( claw, 2K2)-free graphs.

When is the chromatic quasisymmetric function symmetric? On the e-positivity of ( claw, 2K2)-free graphs

Reference 26

Resolution: malformed identifier; doi_truncated, observed 2026-08-11T16:16:24.443489Z

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Observation b05e4512-d72a-42d2-b024-772409d280e3 · outbound

This paper cites personal communication.

When is the chromatic quasisymmetric function symmetric? personal communication

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:16:25.241405Z

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Observation bdf6eea4-11fb-4e17-ba2a-79764194bac7 · outbound

This paper cites The Stanley-Stembridge Conjecture for $\bf 2 + 1 +1$-avoiding unit interval orders: a diagrammatic proof.

When is the chromatic quasisymmetric function symmetric? The Stanley-Stembridge Conjecture for $\bf 2 + 1 +1$-avoiding unit interval orders: a diagrammatic proof

Reference 28

Resolution: verified exact; local_arxiv, observed 2026-08-11T16:16:24.813745Z

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Observation 71693854-fd06-4368-acc4-e23b69c9f453 · outbound

This paper cites SageMath, the Sage Mathematics Software System (Ver.

When is the chromatic quasisymmetric function symmetric? SageMath, the Sage Mathematics Software System (Ver

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:16:25.224654Z

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Observation cf9bac95-1483-428a-b17c-04a3408e63a1 · outbound

This paper cites Chromatic quasisymmetric functions.

When is the chromatic quasisymmetric function symmetric? Chromatic quasisymmetric functions

Reference 30

Resolution: malformed identifier; raw_fallback, observed 2026-08-11T16:16:25.207347Z

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Observation 01a4eb8f-d3a3-47e1-ae6b-841bbc07704f · outbound

This paper cites A symmetric function generalization of the chromatic polynomial of a graph.

When is the chromatic quasisymmetric function symmetric? A symmetric function generalization of the chromatic polynomial of a graph

Reference 31

Resolution: malformed identifier; no resolver link, observed 2026-08-11T16:16:24.340069Z

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Observation 11bd83cb-b481-4b27-bd57-63e4ca05f180 · outbound

This paper cites an unresolved cited work.

When is the chromatic quasisymmetric function symmetric? Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-08-11T16:16:25.190769Z

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Observation 5c64ef4b-c663-4991-afe6-ed0593ff6df8 · outbound

This paper cites On immanants of Jacobi-Trudi matrices and permutations with restricted position.

When is the chromatic quasisymmetric function symmetric? On immanants of Jacobi-Trudi matrices and permutations with restricted position

Reference 33

Resolution: verified exact; doi, observed 2026-08-11T16:16:24.426600Z

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Observation 914f2f21-cefc-4513-b31d-a0b60e7f9bef · outbound

This paper cites doi: 10.37236/12319.

When is the chromatic quasisymmetric function symmetric? doi: 10.37236/12319

Reference 34

Resolution: malformed identifier; doi_truncated, observed 2026-08-11T16:16:24.636341Z

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Observation 32a3f94e-247b-444b-a032-b2c5ad2cdcd2 · outbound

This paper cites The e-positivity of two classes of cycle-chord graphs.

When is the chromatic quasisymmetric function symmetric? The e-positivity of two classes of cycle-chord graphs

Reference 35

Resolution: verified exact; doi, observed 2026-08-11T16:16:24.409009Z

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Observation e3a1b6a5-07b4-4830-ae84-26779895197d · outbound

This paper cites doi: 10.1016/j.ejc.2022.103595.

When is the chromatic quasisymmetric function symmetric? doi: 10.1016/j.ejc.2022.103595

Reference 36

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Observation 77daed99-e7ac-41ae-9817-13aaf70382a8 · outbound

This paper cites A signed $e$-expansion of the chromatic quasisymmetric function.

When is the chromatic quasisymmetric function symmetric? A signed $e$-expansion of the chromatic quasisymmetric function

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-11T16:16:24.355648Z

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Observation 4841cdc1-7fd3-4cf0-a920-725b10d0ebcb · outbound

This paper cites The $e$-positivity of the chromatic symmetric functions and the inverse Kostka matrix.

When is the chromatic quasisymmetric function symmetric? The $e$-positivity of the chromatic symmetric functions and the inverse Kostka matrix

Reference 39

Resolution: verified exact; local_arxiv, observed 2026-08-11T16:16:24.670480Z

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Observation 49ad2335-bc41-4687-89e2-8fe6c4ee6592 · outbound

This paper cites doi: 10.1016/j.aim.2018.02.020.

When is the chromatic quasisymmetric function symmetric? doi: 10.1016/j.aim.2018.02.020

Reference 1001

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Pith citing papers

Observation fb64a629-ca13-425b-9439-b397e4ac866a · inbound

Chromatic quasisymmetric functions for signed graphs cites this paper.

Chromatic quasisymmetric functions for signed graphs When is the chromatic quasisymmetric function symmetric?

Reference 7

Resolution: verified exact; local_arxiv, observed 2026-08-05T15:26:41.403854Z

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