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Paper Citation Record · LEDGER

Combinatorics on bi-$\gamma$-positivity of $1/k$-Eulerian polynomials

As of 13 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 0 inbound Pith citation observations for arXiv:2501.12055.

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

pith.paper-citation-record.v1
2501.12055 v1

Coverage vector

measured 27 of 27 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T17:40:31.281821Z

measured 27 of 27 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+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

27 of 27 outbound references displayed

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  • verified fuzzy19
  • unresolved8
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation f3903a76-3078-45ed-b1d4-8ef66e3e3550 · outbound

This paper cites Athanasiadis, Gamma-positivity in combinatorics and geometr y, S´ em.

Combinatorics on bi-$\gamma$-positivity of $1/k$-Eulerian polynomials Athanasiadis, Gamma-positivity in combinatorics and geometr y, S´ em

Reference 1

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T17:40:31.162777Z digest=sha256:3823eec0bd1d9e25682aad0cbe18cefab23efd7352ca9a7ceb519bd7f77eb200

Observation 5449192c-e756-436f-8e07-5a5bfadfc1e1 · outbound

This paper cites Athanasiadis, Binomial Eulerian polynomials for colored permut ations, J.

Combinatorics on bi-$\gamma$-positivity of $1/k$-Eulerian polynomials Athanasiadis, Binomial Eulerian polynomials for colored permut ations, J

Reference 2

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raw_fallback, observed 2026-08-10T17:40:31.647638Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T17:40:31.168174Z digest=sha256:4200108a577d32d2be0df6602b4641555419531a1d84a5dea8630f8f63a38a7e

Observation 5f24dffe-818e-4b96-937a-5d2895103eaa · outbound

This paper cites Br¨ and´ en, Actions on permutations and unimodality of desce nt polynomials, European J.

Combinatorics on bi-$\gamma$-positivity of $1/k$-Eulerian polynomials Br¨ and´ en, Actions on permutations and unimodality of desce nt polynomials, European J

Reference 3

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raw_fallback, observed 2026-08-10T17:40:31.635873Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T17:40:31.173141Z digest=sha256:d402e9aed945c7b5ba89b6306336016ec4512e68272551718a4f036cad7b730a

Observation cccc381c-e120-46ca-b6e9-45f8a0b757a1 · outbound

This paper cites Br¨ and´ en, Unimodality, log-concavity, real-rootedness and beyond, Handbook of Enumerative Combinatorics , CRC Press Book.

Combinatorics on bi-$\gamma$-positivity of $1/k$-Eulerian polynomials Br¨ and´ en, Unimodality, log-concavity, real-rootedness and beyond, Handbook of Enumerative Combinatorics , CRC Press Book

Reference 4

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raw_fallback, observed 2026-08-10T17:40:31.622534Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T17:40:31.178142Z digest=sha256:ebd543a0872c954437c0fd267e6eb85c2dadf91ecd8fd4209a14c12941ddafe9

Observation 7cefacd3-93f8-4cb3-918e-e806b81330a4 · outbound

This paper cites Br¨ and´ en and L.

Combinatorics on bi-$\gamma$-positivity of $1/k$-Eulerian polynomials Br¨ and´ en and L

Reference 5

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verified fuzzy
raw_fallback, observed 2026-08-10T17:40:31.608760Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T17:40:31.182927Z digest=sha256:1fd19343d91d014987d30cae2828e81dce3331741eec5cf185b01bff7f2a8723

Observation 784fd043-03b7-46ce-9ff1-1330907114ab · outbound

This paper cites an unresolved cited work.

Combinatorics on bi-$\gamma$-positivity of $1/k$-Eulerian polynomials Unresolved cited work

Reference 6

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T17:40:31.187571Z digest=sha256:c0a701c2498fe18a46b511158d0e31a79c50e8a63eb79bacca477d06e55f6c12

Observation 96e16997-6647-46f6-a38b-68739148293b · outbound

This paper cites Chen, A.M.

Combinatorics on bi-$\gamma$-positivity of $1/k$-Eulerian polynomials Chen, A.M

Reference 7

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T17:40:31.192145Z digest=sha256:1d9c99d042f691186915d3d8f5097ae6f348ec980c8394c153532a741ddb3a8b

Observation 27f2583a-e32a-4b34-803c-21a79f55d8dc · outbound

This paper cites Chow, On certain combinatorial expansions of the Eulerian p olynomials, Adv.

Combinatorics on bi-$\gamma$-positivity of $1/k$-Eulerian polynomials Chow, On certain combinatorial expansions of the Eulerian p olynomials, Adv

Reference 8

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raw_fallback, observed 2026-08-10T17:40:31.569466Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T17:40:31.197744Z digest=sha256:b74226a895832fa5f85bf231ec97d312ebd8b0b260e555814e26b4cf657e0cd9

Observation 2cdff7c4-28b6-4d41-8fb8-3d82b5790142 · outbound

This paper cites Colored Multiset Eulerian Polynomials.

Combinatorics on bi-$\gamma$-positivity of $1/k$-Eulerian polynomials Colored Multiset Eulerian Polynomials

Reference 9

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no resolver link, observed 2026-08-10T17:40:31.202789Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T17:40:31.202789Z digest=sha256:94e8a7234b44abbfb27ece26961476a358c79b5af7df68fc162966c836179624

Observation 7b31ad40-7f34-482b-88e8-3c6648dc6a07 · outbound

This paper cites Foata and M.P.

Combinatorics on bi-$\gamma$-positivity of $1/k$-Eulerian polynomials Foata and M.P

Reference 10

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raw_fallback, observed 2026-08-10T17:40:31.557880Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T17:40:31.207966Z digest=sha256:4d27d62ac20e435d94422a3d63bc359c574f83bf7b482218b0471e059c88ecea

Observation 414397c0-8b29-482c-8f3f-36410b23be01 · outbound

This paper cites Foata and V.

Combinatorics on bi-$\gamma$-positivity of $1/k$-Eulerian polynomials Foata and V

Reference 11

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T17:40:31.212699Z digest=sha256:8b4093ca723313287022e66eed4a69bbd0b6dd284cbea1e5df873c9b835b4b69

Observation e3b87149-ab9b-49d2-873a-3ad4b5f4d2dd · outbound

This paper cites Fu and J.

Combinatorics on bi-$\gamma$-positivity of $1/k$-Eulerian polynomials Fu and J

Reference 12

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raw_fallback, observed 2026-08-10T17:40:31.531425Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T17:40:31.216856Z digest=sha256:b41096cee6d092345e0ec8d1c7c169ffd3e9944042ffa8f0c6436d9e4476df44

Observation c383be07-3632-4da1-aa75-c2865e041390 · outbound

This paper cites Gessel and R.

Combinatorics on bi-$\gamma$-positivity of $1/k$-Eulerian polynomials Gessel and R

Reference 13

Resolution
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raw_fallback, observed 2026-08-10T17:40:31.519343Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T17:40:31.221376Z digest=sha256:b0a01890bbf1ff72914049129720c085f487fb9e6385f4661b669e93f6a4f53c

Observation bf14add6-aba9-4039-817d-ff6cf2eef43a · outbound

This paper cites Han, Gamma-positivity of derangement polynomials and binomia l Eulerian polynomials for colored permutations, J.

Combinatorics on bi-$\gamma$-positivity of $1/k$-Eulerian polynomials Han, Gamma-positivity of derangement polynomials and binomia l Eulerian polynomials for colored permutations, J

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T17:40:31.506627Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T17:40:31.225664Z digest=sha256:0142bd1d31833c0d34ff04abde04d8c3a766867a072a823e5403e6cf8b2ef9fa

Observation 89046e36-e611-46f3-90b1-baf684d3be96 · outbound

This paper cites Ji and Z.

Combinatorics on bi-$\gamma$-positivity of $1/k$-Eulerian polynomials Ji and Z

Reference 15

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raw_fallback, observed 2026-08-10T17:40:31.494288Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T17:40:31.229910Z digest=sha256:26faf8cefbe20c13ab7e0b4715d1da72d050d4ac6002a8adc562fa118c1733df

Observation 6d656777-e318-4ff9-9318-ffe0a2e4b725 · outbound

This paper cites an unresolved cited work.

Combinatorics on bi-$\gamma$-positivity of $1/k$-Eulerian polynomials Unresolved cited work

Reference 16

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T17:40:31.234137Z digest=sha256:1d270ab6b7c0f47a1686449744ae9c2cc12498d14d9ffd0e48c65f198588ea0a

Observation 9658662b-fb91-4d74-8e35-4cf73b089ea8 · outbound

This paper cites an unresolved cited work.

Combinatorics on bi-$\gamma$-positivity of $1/k$-Eulerian polynomials Unresolved cited work

Reference 17

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T17:40:31.238177Z digest=sha256:342505de04f4196c39dab13da0d5bd6c78a49d2e97040d5de1e1d2ea68412b01

Observation c5baddb6-e95f-4a99-8836-53b9bea2de7d · outbound

This paper cites an unresolved cited work.

Combinatorics on bi-$\gamma$-positivity of $1/k$-Eulerian polynomials Unresolved cited work

Reference 18

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raw_fallback, observed 2026-08-10T17:40:31.455566Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T17:40:31.242193Z digest=sha256:62b2cb3d3f44b85bc6b978a057a74b5ca66ef1ff8ce04f8831d6e8e3b58f1751

Observation 57431905-3ec8-43d2-a300-c184057f1124 · outbound

This paper cites Lin and J.

Combinatorics on bi-$\gamma$-positivity of $1/k$-Eulerian polynomials Lin and J

Reference 19

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T17:40:31.246495Z digest=sha256:09c179dc4708de0dfe7eca61871f4c68d3fc2a3f3be733f2c79d830f3fe7aa56

Observation 395c8a6c-a7ff-40ce-a678-c3ac3faf1585 · outbound

This paper cites Liu, Statistics on trapezoidal words and k-inversion sequences, Discrete Appl.

Combinatorics on bi-$\gamma$-positivity of $1/k$-Eulerian polynomials Liu, Statistics on trapezoidal words and k-inversion sequences, Discrete Appl

Reference 20

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T17:40:31.251187Z digest=sha256:327db2617ef6b407b91a0dc8553b509b19a73241a5f65d564d07163ea0fac073

Observation a0076619-f606-4e6d-ba56-f11bf3adab56 · outbound

This paper cites Ma and K.

Combinatorics on bi-$\gamma$-positivity of $1/k$-Eulerian polynomials Ma and K

Reference 21

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T17:40:31.255535Z digest=sha256:88b5896be0e2957b867108eb85c0798c2c2e9d9aaea5a6ddf2af7e399e4a27bc

Observation 7a32e94c-4782-48c4-bb3a-a7fe993d07ee · outbound

This paper cites an unresolved cited work.

Combinatorics on bi-$\gamma$-positivity of $1/k$-Eulerian polynomials Unresolved cited work

Reference 22

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T17:40:31.259470Z digest=sha256:86ef8097883a203d49374a0d95c3077d732ee6e8b5312830a796c77a03abc057

Observation 42f23287-4c04-4172-b6d0-92f6f062fb32 · outbound

This paper cites an unresolved cited work.

Combinatorics on bi-$\gamma$-positivity of $1/k$-Eulerian polynomials Unresolved cited work

Reference 23

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raw_fallback, observed 2026-08-10T17:40:31.383122Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T17:40:31.264663Z digest=sha256:d5513808d25227f5d7f3562e1abeb0ab9954309d380d0138c5477f6b545563ac

Observation a8122bd9-7fa8-4120-bbb6-de00539f9ac1 · outbound

This paper cites Ma and T.

Combinatorics on bi-$\gamma$-positivity of $1/k$-Eulerian polynomials Ma and T

Reference 24

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raw_fallback, observed 2026-08-10T17:40:31.370751Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T17:40:31.269014Z digest=sha256:d8e8a74bdf4b5b31752534e676841c8f77a36321b6710a612bce6dda99dde382

Observation ded6d3ed-49e0-4521-a7dc-9ed46eeefe9c · outbound

This paper cites Savage, The mathematics of lecture hall partitions, J.

Combinatorics on bi-$\gamma$-positivity of $1/k$-Eulerian polynomials Savage, The mathematics of lecture hall partitions, J

Reference 25

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raw_fallback, observed 2026-08-10T17:40:31.358367Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T17:40:31.272879Z digest=sha256:f8fcc39c4c4d5668012d3d1ba6abbd7becf0ae906e9fd20f69b1c362beefac64

Observation 4ff73352-5ac5-4156-b68e-f27aaec437cc · outbound

This paper cites Savage and G.

Combinatorics on bi-$\gamma$-positivity of $1/k$-Eulerian polynomials Savage and G

Reference 26

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raw_fallback, observed 2026-08-10T17:40:31.345200Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T17:40:31.276879Z digest=sha256:ff8f791f81a616a49f1712fb5f216007c8ba609aac9dae9b6e41d9070362d6a9

Observation afb19b78-e617-40a9-baff-3b0881a622e9 · outbound

This paper cites an unresolved cited work.

Combinatorics on bi-$\gamma$-positivity of $1/k$-Eulerian polynomials Unresolved cited work

Reference 27

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raw_fallback, observed 2026-08-10T17:40:31.331520Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T17:40:31.281821Z digest=sha256:884162c06f7daf31d3bfca89c0cb1953b11bbb555110322e4a8eb3a8ee084bf2

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