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Paper Citation Record · LEDGER

Counting the number of group orbits by marrying the Burnside process with importance sampling

As of 13 August 2026, this Paper Citation Record lists 43 of 43 outbound references and 2 inbound Pith citation observations for arXiv:2501.11731.

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

pith.paper-citation-record.v1
2501.11731 v2

Coverage vector

measured 43 of 43 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T17:59:53.059814Z

measured 45 of 45 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-22T12:22:17.215037Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-22T12:24:51.294376Z

Reference resolution

43 of 43 outbound references displayed

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  • verified fuzzy29
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d0097ada-3ba4-4f0e-9516-9a441d058360 · outbound

This paper cites Reversible Markov chains and random walks on graphs.

Counting the number of group orbits by marrying the Burnside process with importance sampling Reversible Markov chains and random walks on graphs

Reference 1

Resolution
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Source-reported events for the cited work

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Observation d05fdb80-c29b-48ff-a7d8-3efdb39d21c9 · outbound

This paper cites An algorithm for uniform generation of unlabeled trees (P\'olya trees), with an extension of Cayley's formula.

Counting the number of group orbits by marrying the Burnside process with importance sampling An algorithm for uniform generation of unlabeled trees (P\'olya trees), with an extension of Cayley's formula

Reference 2

Resolution
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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation 4bdf6168-11df-499d-a5c9-247c55292ad5 · outbound

This paper cites an unresolved cited work.

Counting the number of group orbits by marrying the Burnside process with importance sampling Unresolved cited work

Reference 3

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation a378d7ac-afb1-4dc3-bf35-d10f61d17cf9 · outbound

This paper cites Estimating the number of species: a review.

Counting the number of group orbits by marrying the Burnside process with importance sampling Estimating the number of species: a review

Reference 4

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 7fefb98c-b588-4387-af43-9806c3e5c108 · outbound

This paper cites Inference in hidden Markov models.

Counting the number of group orbits by marrying the Burnside process with importance sampling Inference in hidden Markov models

Reference 5

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 1a287f21-b3f4-42ae-a4d1-7d90cb81b229 · outbound

This paper cites The sample size required in impor- tance sampling.

Counting the number of group orbits by marrying the Burnside process with importance sampling The sample size required in impor- tance sampling

Reference 6

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 65cb52e8-09e5-44f1-9b5d-b4c8927976a5 · outbound

This paper cites Mixing times for Burnside processes.

Counting the number of group orbits by marrying the Burnside process with importance sampling Mixing times for Burnside processes

Reference 7

Resolution
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Source-reported events for the cited work

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Observation 89ef4ca0-dbcb-4843-8e9d-9789ef9ec7b9 · outbound

This paper cites Analysis of a Bose-Einstein Markov chain.

Counting the number of group orbits by marrying the Burnside process with importance sampling Analysis of a Bose-Einstein Markov chain

Reference 8

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 794baabf-9b1c-47b7-b67a-89b110f503be · outbound

This paper cites Statistical enumeration of groups by double cosets.

Counting the number of group orbits by marrying the Burnside process with importance sampling Statistical enumeration of groups by double cosets

Reference 9

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 3a35a867-8c69-4fe5-b175-a0bddf12aff3 · outbound

This paper cites Supercharacter formulas for pattern groups.

Counting the number of group orbits by marrying the Burnside process with importance sampling Supercharacter formulas for pattern groups

Reference 10

Resolution
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Source-reported events for the cited work

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Observation c7f319f5-3d04-4899-ac6d-d9fe5886ec50 · outbound

This paper cites Poisson approximation for large permutation groups.

Counting the number of group orbits by marrying the Burnside process with importance sampling Poisson approximation for large permutation groups

Reference 11

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 18020aec-284f-4927-a587-3ad816d9ae66 · outbound

This paper cites Hahn polynomials and the Burnside pro- cess.

Counting the number of group orbits by marrying the Burnside process with importance sampling Hahn polynomials and the Burnside pro- cess

Reference 12

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation e77c1589-1aa1-4236-968f-8f7317fb0771 · outbound

This paper cites an unresolved cited work.

Counting the number of group orbits by marrying the Burnside process with importance sampling Unresolved cited work

Reference 13

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 2b7848c7-6c78-4e28-b0bb-9ec6317abdb4 · outbound

This paper cites an unresolved cited work.

Counting the number of group orbits by marrying the Burnside process with importance sampling Unresolved cited work

Reference 14

Resolution
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Source-reported events for the cited work

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Observation 7a1efdec-0712-4bf4-883f-e9f529653765 · outbound

This paper cites Burnside process.

Counting the number of group orbits by marrying the Burnside process with importance sampling Burnside process

Reference 15

Resolution
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Source-reported events for the cited work

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Observation fc98575b-99c9-4b49-8c93-95fff7bc271e · outbound

This paper cites A., and Jerrum, M.

Counting the number of group orbits by marrying the Burnside process with importance sampling A., and Jerrum, M

Reference 16

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 58eea3dc-1487-47a9-a53a-8ec102c6ed7b · outbound

This paper cites an unresolved cited work.

Counting the number of group orbits by marrying the Burnside process with importance sampling Unresolved cited work

Reference 17

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation fc899d9a-8d8d-492b-86fd-8d0af43b7128 · outbound

This paper cites M., and Handscomb, D.

Counting the number of group orbits by marrying the Burnside process with importance sampling M., and Handscomb, D

Reference 18

Resolution
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Source-reported events for the cited work

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Observation c54e3c47-adc0-4c39-b1cf-97fbfda53168 · outbound

This paper cites Enumerating p-groups.

Counting the number of group orbits by marrying the Burnside process with importance sampling Enumerating p-groups

Reference 19

Resolution
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Source-reported events for the cited work

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Observation 1a5679b4-23fd-43b0-b6a0-0f7b656b9b06 · outbound

This paper cites Uniform sampling modulo a group of symmetries using Markov chain simulation.

Counting the number of group orbits by marrying the Burnside process with importance sampling Uniform sampling modulo a group of symmetries using Markov chain simulation

Reference 20

Resolution
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Source-reported events for the cited work

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Observation ddff13d2-0092-4423-be68-ba500359231c · outbound

This paper cites Computational P´ olya theory.

Counting the number of group orbits by marrying the Burnside process with importance sampling Computational P´ olya theory

Reference 21

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 3a461811-d6df-45c1-8221-6d94158369ab · outbound

This paper cites Counting, sampling and integrating: algorithms and complex- ity.

Counting the number of group orbits by marrying the Burnside process with importance sampling Counting, sampling and integrating: algorithms and complex- ity

Reference 22

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Observation a3f5e714-d57a-4979-b66a-636b91d4f377 · outbound

This paper cites R., V aliant, L.

Counting the number of group orbits by marrying the Burnside process with importance sampling R., V aliant, L

Reference 23

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation dd8b42c9-d029-4217-957c-baf686ec69dc · outbound

This paper cites an unresolved cited work.

Counting the number of group orbits by marrying the Burnside process with importance sampling Unresolved cited work

Reference 24

Resolution
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Source-reported events for the cited work

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Observation a3efdb14-26ab-472a-9510-0201eb15d588 · outbound

This paper cites G., and Snell, J.

Counting the number of group orbits by marrying the Burnside process with importance sampling G., and Snell, J

Reference 25

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 17e406e5-a8c2-49c9-8a2b-994532b9c3ec · outbound

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Counting the number of group orbits by marrying the Burnside process with importance sampling Unresolved cited work

Reference 26

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 00c29f8a-6bd2-472e-8e31-b09b514b8ae7 · outbound

This paper cites Importance sampling for families of distributions.

Counting the number of group orbits by marrying the Burnside process with importance sampling Importance sampling for families of distributions

Reference 27

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation db8f6c10-6ea1-4e08-af42-7cfdd2caa347 · outbound

This paper cites Constructing modules of algebra groups.

Counting the number of group orbits by marrying the Burnside process with importance sampling Constructing modules of algebra groups

Reference 28

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation ab4d7511-081c-4f83-a053-4c73213f66c6 · outbound

This paper cites Combinatorial methods of character enumeration for the unitriangular group.

Counting the number of group orbits by marrying the Burnside process with importance sampling Combinatorial methods of character enumeration for the unitriangular group

Reference 29

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation ba6768c2-0fca-468d-99a5-f47909f8fdc4 · outbound

This paper cites Mixing times of a Burnside process Markov chain on set partitions.

Counting the number of group orbits by marrying the Burnside process with importance sampling Mixing times of a Burnside process Markov chain on set partitions

Reference 30

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation ef2a7d64-60fb-4e44-ac6a-cddbd6d69786 · outbound

This paper cites On Higman's $k(U_n(\mathbb{F}_q))$ conjecture.

Counting the number of group orbits by marrying the Burnside process with importance sampling On Higman's $k(U_n(\mathbb{F}_q))$ conjecture

Reference 31

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation fa2d846e-175f-4ee4-9555-d85b13cd0bf5 · outbound

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Counting the number of group orbits by marrying the Burnside process with importance sampling Unresolved cited work

Reference 32

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 3acf1a29-b32f-4cdf-8df3-0a191568f987 · outbound

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Counting the number of group orbits by marrying the Burnside process with importance sampling Unresolved cited work

Reference 33

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Source-reported events for the cited work

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Observation f72f6329-7565-431e-b02c-9a4a8ca67610 · outbound

This paper cites Mixing times for the commuting chain on CA groups.Journal of Theoretical Probability 35, 1 (2022), 457–483.

Counting the number of group orbits by marrying the Burnside process with importance sampling Mixing times for the commuting chain on CA groups.Journal of Theoretical Probability 35, 1 (2022), 457–483

Reference 34

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation a5f4b38d-207c-40ec-93c3-d2f92bf66072 · outbound

This paper cites P., and Casella, G.

Counting the number of group orbits by marrying the Burnside process with importance sampling P., and Casella, G

Reference 35

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation e6611571-c98e-4c9b-a3e9-ad0acdbf1a2e · outbound

This paper cites Algorithms for random generation and counting: a Markov chain approach.

Counting the number of group orbits by marrying the Burnside process with importance sampling Algorithms for random generation and counting: a Markov chain approach

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T17:59:53.316819Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-10T17:59:53.034567Z digest=sha256:768f850c8bf6a5500377defca5bb9eed1ed868ee4a3c9d64802d41ec1f65aacc

Observation 119efe2b-cb48-4767-914f-ab2aa810a655 · outbound

This paper cites Approximate counting, uniform genera- tion and rapidly mixing Markov chains.

Counting the number of group orbits by marrying the Burnside process with importance sampling Approximate counting, uniform genera- tion and rapidly mixing Markov chains

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T17:59:53.304512Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 2e591a6a-45a3-4ec3-a2e3-d039a20a4701 · outbound

This paper cites Upper bounds on the number of conjugacy classes in unitri- angular groups.

Counting the number of group orbits by marrying the Burnside process with importance sampling Upper bounds on the number of conjugacy classes in unitri- angular groups

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T17:59:53.291261Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-10T17:59:53.041346Z digest=sha256:f7b420557090c930144bea333ff43be05b9c821331dee4813481cf75127202c3

Observation f14aa5e1-fb53-4779-bf65-67dd6ac64e30 · outbound

This paper cites an unresolved cited work.

Counting the number of group orbits by marrying the Burnside process with importance sampling Unresolved cited work

Reference 39

Resolution
unresolved
raw_fallback, observed 2026-08-10T17:59:53.276456Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-10T17:59:53.044577Z digest=sha256:eeb5da4d76daa15f3afea454a7764b64a3a8c734edf56f70c34e7707cd87b2bb

Observation 05ae612d-30dc-4a54-a573-cd94c6d34b41 · outbound

This paper cites an unresolved cited work.

Counting the number of group orbits by marrying the Burnside process with importance sampling Unresolved cited work

Reference 40

Resolution
unresolved
raw_fallback, observed 2026-08-10T17:59:53.263562Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-10T17:59:53.048463Z digest=sha256:4ca9675b162524747414f88bbac13d76b5dd44ec719b0ac69956a5615312d00f

Observation d7519008-e9e4-40a2-939d-e48768ce9181 · outbound

This paper cites Importance sampling: Applications in communications and detection.

Counting the number of group orbits by marrying the Burnside process with importance sampling Importance sampling: Applications in communications and detection

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T17:59:53.250954Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-10T17:59:53.052467Z digest=sha256:bae8eff026d46e7354f8267b6a8c79ba438d96570fb67b2285467d8af3181637

Observation 2f1bac29-3fc8-4c68-98b5-7a30660ad667 · outbound

This paper cites Conjugacy classes in unitriangular matrices.

Counting the number of group orbits by marrying the Burnside process with importance sampling Conjugacy classes in unitriangular matrices

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T17:59:53.237784Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-10T17:59:53.056050Z digest=sha256:60845b2044e3fc84bfa924b214bd2c56b636a7eef372d3554b26304a11f44e12

Observation 6bd76580-1fea-4d80-89cc-5eee051a1962 · outbound

This paper cites Mixing time of the commuting chain on the symmetric group.

Counting the number of group orbits by marrying the Burnside process with importance sampling Mixing time of the commuting chain on the symmetric group

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T17:59:53.223078Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-10T17:59:53.059814Z digest=sha256:311b646d30389c760d9e7e4075c37074c3ea248a02f156fb19c8e6db474062d7

Pith citing papers

Observation 9ae040f9-8b8c-407f-83db-80fc78b93cce · inbound

Estimating the size of a set using cascading exclusion cites this paper.

Estimating the size of a set using cascading exclusion Counting the number of group orbits by marrying the Burnside process with importance sampling

Reference 21

Resolution
verified exact
arxiv_id, observed 2026-05-19T00:02:54.146378Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-05-19T00:02:04.256336Z digest=sha256:66524c56920460df0602794daea9968fb374d61448c5944cd7104d8764844173

Observation 6f7b6fba-b243-4e48-bedb-e94b4186334d · inbound

The dual Burnside process cites this paper.

The dual Burnside process Counting the number of group orbits by marrying the Burnside process with importance sampling

Reference 18

Resolution
verified exact
arxiv_id, observed 2026-05-22T12:24:51.297823Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-05-22T12:22:17.215037Z digest=sha256:b80817a34bb5db9c86f442247ed404eb6ea428edc23e5f18b8ccad75598e170d