Paper Citation Record · LEDGER

Ramanujan Graphs and Interlacing Families

As of 18 August 2026, this Paper Citation Record lists 53 of 53 outbound references and 0 inbound Pith citation observations for arXiv:2412.20721.

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

pith.paper-citation-record.v1
2412.20721 v1

Coverage vector

measured 53 of 53 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T23:19:40.076313Z

measured 53 of 53 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

53 of 53 outbound references displayed

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verified fuzzy42
unresolved6
parse uncertain0
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External citation measurements

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Outbound references

Observation 5956cd60-1974-44b0-964b-b73f565b4ed6 · outbound

This paper cites The monotone circuit complexity of boolean functions.

Ramanujan Graphs and Interlacing Families The monotone circuit complexity of boolean functions

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.814160Z

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Observation 77d9e492-a5e6-47e1-8be7-a74bc495e599 · outbound

This paper cites Stable multivariate generalizations of matching polynomials.

Ramanujan Graphs and Interlacing Families Stable multivariate generalizations of matching polynomials

Reference 2

Resolution: verified exact; local_arxiv, observed 2026-08-10T23:19:40.349016Z

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Observation 2abcd8f2-0e03-41cb-b867-e74de45c5aad · outbound

This paper cites The Kadison-Singer Problem for Strongly Rayleigh Measures and Applications to Asymmetric TSP.

Ramanujan Graphs and Interlacing Families The Kadison-Singer Problem for Strongly Rayleigh Measures and Applications to Asymmetric TSP

Reference 3

Resolution: verified exact; local_arxiv, observed 2026-08-10T23:19:40.332881Z

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Observation ea4a3d40-ee2e-4570-a025-550cfe1eee36 · outbound

This paper cites Approximating the largest root and applications to interlacing families.

Ramanujan Graphs and Interlacing Families Approximating the largest root and applications to interlacing families

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.804623Z

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Observation a4f082ca-7826-472f-974e-6fd7510f472d · outbound

This paper cites $S$-transform in Finite Free Probability.

Ramanujan Graphs and Interlacing Families $S$-transform in Finite Free Probability

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-10T23:19:39.892932Z

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Observation 1484fa07-43bc-4b13-8291-eccb1d5231e6 · outbound

This paper cites Fin ite free cumulants: multiplicative convolutions, genus expansion and inﬁnitesimal distribu tions.

Ramanujan Graphs and Interlacing Families Fin ite free cumulants: multiplicative convolutions, genus expansion and inﬁnitesimal distribu tions

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.794185Z

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Observation 0fc0047e-7d3c-45b2-838d-f26500e4d1e0 · outbound

This paper cites Cumulants for ﬁnite free c onvolution.

Ramanujan Graphs and Interlacing Families Cumulants for ﬁnite free c onvolution

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.782689Z

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Observation 9d073d40-6370-48b4-80ec-7b8bd8adce4d · outbound

This paper cites Edge rigidity and universality of random regular graphs of intermediate de gree.

Ramanujan Graphs and Interlacing Families Edge rigidity and universality of random regular graphs of intermediate de gree

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.771078Z

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Observation 8a26e3f8-2300-4c80-8dcc-361a21f885f3 · outbound

This paper cites Lifts, discrepancy and nearly optim al spectral gap.

Ramanujan Graphs and Interlacing Families Lifts, discrepancy and nearly optim al spectral gap

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.759350Z

Source-reported events for the cited work

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Observation e1070649-d84b-4688-a753-b58e742a519e · outbound

This paper cites The lee-yang and p´ olya-schur programs.

Ramanujan Graphs and Interlacing Families The lee-yang and p´ olya-schur programs

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.747511Z

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Observation ff472b08-29af-4875-8b07-ae01b163b739 · outbound

This paper cites The lee-yang and p´ olya-schur programs.

Ramanujan Graphs and Interlacing Families The lee-yang and p´ olya-schur programs

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.734746Z

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Observation 39bdef6c-99ad-45fd-a637-77c57afd6a72 · outbound

This paper cites A new proof of Friedman's second eigenvalue Theorem and its extension to random lifts.

Ramanujan Graphs and Interlacing Families A new proof of Friedman's second eigenvalue Theorem and its extension to random lifts

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-10T23:19:39.920338Z

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Observation 66c81abb-6e44-4868-b150-241f5ea04022 · outbound

This paper cites Eigenvalues of random lift s and polynomials of random permutation matrices.

Ramanujan Graphs and Interlacing Families Eigenvalues of random lift s and polynomials of random permutation matrices

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.722840Z

Source-reported events for the cited work

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Observation 855289a3-0914-4232-b88c-5aca86d7c6fb · outbound

This paper cites On Akemann-Weaver Conjecture.

Ramanujan Graphs and Interlacing Families On Akemann-Weaver Conjecture

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-10T23:19:39.928190Z

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Unavailable: canonical work link unavailable.

Observation c5aa375c-6e9b-4d64-8c6c-580dc8f9a7d3 · outbound

This paper cites A new approach to strong convergence.

Ramanujan Graphs and Interlacing Families A new approach to strong convergence

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-10T23:19:39.932103Z

Source-reported events for the cited work

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Observation 994994f0-7c05-49e4-9f2b-4de2928103fd · outbound

This paper cites Ramanujan graphs and shimura curves, 2006.

Ramanujan Graphs and Interlacing Families Ramanujan graphs and shimura curves, 2006

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.712260Z

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Observation bd10d6c3-cb88-467c-8c4f-fe4f299cb1cb · outbound

This paper cites Ramanujan graphs in polynomial time.

Ramanujan Graphs and Interlacing Families Ramanujan graphs in polynomial time

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.701332Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 6930df67-10ee-49f1-b9ab-2979081fcdf7 · outbound

This paper cites Random matrices, magic squar es and matching polynomials.

Ramanujan Graphs and Interlacing Families Random matrices, magic squar es and matching polynomials

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.691894Z

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Observation 128bbe75-59c9-4889-878d-9913d274183a · outbound

This paper cites On the eigenvalues of random matrices.

Ramanujan Graphs and Interlacing Families On the eigenvalues of random matrices

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.681736Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 9c17e973-2d63-46ee-81e3-b9aea12b967a · outbound

This paper cites Some geometric aspects of graphs and their eig enfunctions.

Ramanujan Graphs and Interlacing Families Some geometric aspects of graphs and their eig enfunctions

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.672905Z

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Observation 3077e11e-b818-47d4-9cb4-ceaed9a4227e · outbound

This paper cites Relative expanders or weakly relatively ramanuj an graphs.

Ramanujan Graphs and Interlacing Families Relative expanders or weakly relatively ramanuj an graphs

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.661417Z

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Observation ec6f110b-a561-4b7b-88e3-fc939528182d · outbound

This paper cites A proof of Alon ’s second eigenvalue conjecture and related p roblems.

Ramanujan Graphs and Interlacing Families A proof of Alon ’s second eigenvalue conjecture and related p roblems

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.649286Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 4ca8f3d9-6707-4365-bfd5-6af9492dea8f · outbound

This paper cites On the Relativized Alon Second Eigenvalue Conjecture I: Main Theorems, Examples, and Outline of Proof.

Ramanujan Graphs and Interlacing Families On the Relativized Alon Second Eigenvalue Conjecture I: Main Theorems, Examples, and Outline of Proof

Reference 23

Resolution: verified exact; local_arxiv, observed 2026-08-10T23:19:40.168946Z

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Observation d6029a4d-7b41-4ffd-bc03-d9ba41a27cc6 · outbound

This paper cites On the matching polynomial of a graph.

Ramanujan Graphs and Interlacing Families On the matching polynomial of a graph

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.638108Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 5e350654-5675-46bb-85d2-a04923a5578a · outbound

This paper cites Crystallization of random matrix o rbits.

Ramanujan Graphs and Interlacing Families Crystallization of random matrix o rbits

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.627879Z

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Observation 9300f1b6-60e9-470a-8b7d-72384d4fb5b6 · outbound

This paper cites On the spectrum of graphs and their universal covering.

Ramanujan Graphs and Interlacing Families On the spectrum of graphs and their universal covering

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.616825Z

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Observation 22a4f78c-8445-44dd-950d-a40c836e140d · outbound

This paper cites A theory of singular values for ﬁnite free prob ability.

Ramanujan Graphs and Interlacing Families A theory of singular values for ﬁnite free prob ability

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.606565Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 046cd92f-71b9-4631-9058-20c4f9edb9ee · outbound

This paper cites Ramanujan coverings o f graphs.

Ramanujan Graphs and Interlacing Families Ramanujan coverings o f graphs

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.596111Z

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Observation 17473ba3-5763-4712-9b8b-1bfedc4bd01e · outbound

This paper cites Theory of monomer-dimer systems.

Ramanujan Graphs and Interlacing Families Theory of monomer-dimer systems

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.585525Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation da6d869a-46af-49cd-b50e-4af745ca14f2 · outbound

This paper cites Near optimal spectral gaps for hyp erbolic surfaces.

Ramanujan Graphs and Interlacing Families Near optimal spectral gaps for hyp erbolic surfaces

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.572877Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 2b7821e0-609d-4b9b-a096-67c8c6f1ed4b · outbound

This paper cites Optimal Eigenvalue Rigidity of Random Regular Graphs.

Ramanujan Graphs and Interlacing Families Optimal Eigenvalue Rigidity of Random Regular Graphs

Reference 31

Resolution: verified exact; local_arxiv, observed 2026-08-10T23:19:40.153939Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c49456c2-8d24-484c-9f75-843eaa2b2c4a · outbound

This paper cites Edge Universality of Sparse Random Matrices.

Ramanujan Graphs and Interlacing Families Edge Universality of Sparse Random Matrices

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-10T23:19:39.994865Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b859fb44-c723-417e-920d-d96efa8cd8bf · outbound

This paper cites Random matrix theory and ζ (1/2+ it).

Ramanujan Graphs and Interlacing Families Random matrix theory and ζ (1/2+ it)

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.561362Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 3c72c891-2e8e-4725-a65a-213f788da289 · outbound

This paper cites Discrete groups, expanding graphs and invariant measures , volume 125.

Ramanujan Graphs and Interlacing Families Discrete groups, expanding graphs and invariant measures , volume 125

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.550873Z

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Observation f9c20f39-0501-49ac-9eab-78d785bccda9 · outbound

This paper cites Not every uniform tree covers ramanujan graphs.

Ramanujan Graphs and Interlacing Families Not every uniform tree covers ramanujan graphs

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.540902Z

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Observation 4da93a74-0e61-49ac-bd4e-f06c3ce9ffb6 · outbound

This paper cites Ramanuj an graphs.

Ramanujan Graphs and Interlacing Families Ramanuj an graphs

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.529898Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation af748f36-295c-4025-b3d3-dd775500b7af · outbound

This paper cites The solution of the kadison- singer problem.

Ramanujan Graphs and Interlacing Families The solution of the kadison- singer problem

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.518864Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 4fe76c4d-a086-491e-ab09-d51de72b742c · outbound

This paper cites Polynomial convolutions and (finite) free probability.

Ramanujan Graphs and Interlacing Families Polynomial convolutions and (finite) free probability

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-10T23:19:40.017114Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation de65a3c7-cbae-4ca2-8038-f36d75948e9a · outbound

This paper cites Ramanu jan graphs and the solution of the kadison-singer problem.

Ramanujan Graphs and Interlacing Families Ramanu jan graphs and the solution of the kadison-singer problem

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.507203Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 60cfc2b4-8714-4224-91aa-cb0364c9c0c3 · outbound

This paper cites Interla cing families i: Bipartite ramanujan graphs of all degrees.

Ramanujan Graphs and Interlacing Families Interla cing families i: Bipartite ramanujan graphs of all degrees

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.496067Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 50be58b5-8586-49f6-a796-86a02fe69e14 · outbound

This paper cites Interla cing families ii: Mixed characteristic polynomials and the kadison—singer problem.

Ramanujan Graphs and Interlacing Families Interla cing families ii: Mixed characteristic polynomials and the kadison—singer problem

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.484040Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 90df3ddc-bcb9-4d9e-bcb0-a25cfba338c4 · outbound

This paper cites Interla cing families iv: Bipartite ramanujan graphs of all sizes.

Ramanujan Graphs and Interlacing Families Interla cing families iv: Bipartite ramanujan graphs of all sizes

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.472375Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 85b497b5-d91c-4b3e-b673-2751bf8809eb · outbound

This paper cites Finite fr ee convolutions of polynomials.

Ramanujan Graphs and Interlacing Families Finite fr ee convolutions of polynomials

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.460541Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation f45ab26f-fac6-4fe7-9645-753c3b67b2cb · outbound

This paper cites Explicit group-theoretical co nstructions of combi- natorial schemes and their application to the design of expanders a nd concentrators.

Ramanujan Graphs and Interlacing Families Explicit group-theoretical co nstructions of combi- natorial schemes and their application to the design of expanders a nd concentrators

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.450001Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 83d8308b-8e38-436a-9a26-72000aa8a08a · outbound

This paper cites The expected eigenvalue distribution of a larg e regular graph.

Ramanujan Graphs and Interlacing Families The expected eigenvalue distribution of a larg e regular graph

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.438578Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation e57a55d2-fc1b-40c3-b883-6f33afeed942 · outbound

This paper cites The distribution o f the largest nontrivial eigenvalues in families of random regular graphs.

Ramanujan Graphs and Interlacing Families The distribution o f the largest nontrivial eigenvalues in families of random regular graphs

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.428528Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 575744be-97b6-414e-a50e-c40c101d5b91 · outbound

This paper cites $X$-Ramanujan Graphs.

Ramanujan Graphs and Interlacing Families $X$-Ramanujan Graphs

Reference 47

Resolution: verified exact; local_arxiv, observed 2026-08-10T23:19:40.114972Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 13b3b0e7-6b6d-4333-8709-d208f03ce0a1 · outbound

This paper cites Expansion of random graphs: New proofs, new r esults.

Ramanujan Graphs and Interlacing Families Expansion of random graphs: New proofs, new r esults

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.419043Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 4008a32e-1182-4032-b65c-c6a000a8b7c4 · outbound

This paper cites Mixed determinants and the kadison–singer problem.

Ramanujan Graphs and Interlacing Families Mixed determinants and the kadison–singer problem

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.409038Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation f9b6d051-185c-4ec1-a747-651b9e0d300a · outbound

This paper cites Colloque de combinatoire ´ enum´ erative.

Ramanujan Graphs and Interlacing Families Colloque de combinatoire ´ enum´ erative

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.398364Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation df55988e-718e-4bfa-96bc-e81e9e91a193 · outbound

This paper cites Limit laws for random matrices and free product s.

Ramanujan Graphs and Interlacing Families Limit laws for random matrices and free product s

Reference 51

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.386142Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation be8c7e2d-960e-48de-ae36-9da77be8695e · outbound

This paper cites On the location of the roots of certain types of polynomials.

Ramanujan Graphs and Interlacing Families On the location of the roots of certain types of polynomials

Reference 52

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:19:40.374749Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation d0e5d22d-0ee7-4fd4-98c2-5f5faf30f9ad · outbound

This paper cites Models of random regular graphs.

Ramanujan Graphs and Interlacing Families Models of random regular graphs

Reference 53

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