@article{Edmonds1965,
  author = {Edmonds, Jack},
  title = {Maximum Matching and a Polyhedron with {0,1}-Vertices},
  journal = {Journal of Research of the National Bureau of Standards, Section B},
  volume = {69B},
  number = {1--2},
  pages = {125--130},
  year = {1965},
  doi = {10.6028/jres.069B.013},
  url = {https://nvlpubs.nist.gov/nistpubs/jres/69B/jresv69Bn1-2p125_A1b.pdf}
}

@article{Valiant1979,
  author = {Valiant, Leslie G.},
  title = {The Complexity of Computing the Permanent},
  journal = {Theoretical Computer Science},
  volume = {8},
  number = {2},
  pages = {189--201},
  year = {1979},
  doi = {10.1016/0304-3975(79)90044-6},
  url = {https://www.cs.bu.edu/faculty/gacs/courses/cs535/papers/Valiant_permanent.pdf}
}

@article{Barvinok1999,
  author = {Barvinok, Alexander},
  title = {Polynomial Time Algorithms to Approximate Permanents and Mixed Discriminants Within a Simply Exponential Factor},
  journal = {Random Structures \& Algorithms},
  volume = {14},
  number = {1},
  pages = {29--61},
  year = {1999},
  doi = {10.1002/(SICI)1098-2418(1999010)14:1<29::AID-RSA2>3.0.CO;2-X},
  note = {Section locator refers to the author preprint},
  url = {https://sites.lsa.umich.edu/barvinok/wp-content/uploads/sites/1434/2025/05/permanent.pdf}
}

@article{LinialSamorodnitskyWigderson2000,
  author = {Linial, Nathan and Samorodnitsky, Alex and Wigderson, Avi},
  title = {A Deterministic Strongly Polynomial Algorithm for Matrix Scaling and Approximate Permanents},
  journal = {Combinatorica},
  volume = {20},
  number = {4},
  pages = {545--568},
  year = {2000},
  doi = {10.1007/s004930070007},
  note = {Theorem locator refers to the author version},
  url = {https://www.math.ias.edu/~avi/PUBLICATIONS/MYPAPERS/LSW98/lsw00.pdf}
}

@article{JerrumSinclairVigoda2004,
  author = {Jerrum, Mark and Sinclair, Alistair and Vigoda, Eric},
  title = {A Polynomial-Time Approximation Algorithm for the Permanent of a Matrix with Nonnegative Entries},
  journal = {Journal of the ACM},
  volume = {51},
  number = {4},
  pages = {671--697},
  year = {2004},
  doi = {10.1145/1008731.1008738},
  url = {https://doi.org/10.1145/1008731.1008738}
}

@article{Barvinok2017,
  author = {Barvinok, Alexander},
  title = {Approximating Permanents and Hafnians},
  journal = {Discrete Analysis},
  year = {2017},
  volume = {2017},
  number = {2},
  pages = {1--34},
  doi = {10.19086/da.1244},
  url = {https://discreteanalysisjournal.com/article/1244-approximating-permanents-and-hafnians},
  eprint = {1601.07518v5},
  archivePrefix = {arXiv},
  primaryClass = {math.CO},
  note = {Theorem locator refers to the final arXiv version 1601.07518v5,
          13 January 2017}
}

@inproceedings{AnariOveisGharanVinzant2018,
  author = {Anari, Nima and Oveis Gharan, Shayan and Vinzant, Cynthia},
  title = {Log-Concave Polynomials, Entropy, and a Deterministic Approximation Algorithm for Counting Bases of Matroids},
  booktitle = {2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)},
  pages = {35--46},
  publisher = {IEEE},
  year = {2018},
  doi = {10.1109/FOCS.2018.00013},
  url = {https://ieee-focs.org/FOCS-2018-Papers/pdfs/59f035.pdf}
}

@article{PadbergRao1982,
  author = {Padberg, Manfred W. and Rao, M. R.},
  title = {Odd Minimum Cut-Sets and {$b$}-Matchings},
  journal = {Mathematics of Operations Research},
  volume = {7},
  number = {1},
  pages = {67--80},
  year = {1982},
  doi = {10.1287/moor.7.1.67},
  url = {https://pubsonline.informs.org/doi/10.1287/moor.7.1.67}
}

@article{Jaynes1957,
  author = {Jaynes, Edwin T.},
  title = {Information Theory and Statistical Mechanics},
  journal = {Physical Review},
  volume = {106},
  number = {4},
  pages = {620--630},
  year = {1957},
  doi = {10.1103/PhysRev.106.620},
  url = {https://doi.org/10.1103/PhysRev.106.620}
}

@inproceedings{SinghVishnoi2014,
  author = {Singh, Mohit and Vishnoi, Nisheeth K.},
  title = {Entropy, Optimization and Counting},
  booktitle = {Proceedings of the Forty-Sixth Annual ACM Symposium on Theory of Computing},
  pages = {50--59},
  publisher = {ACM},
  year = {2014},
  doi = {10.1145/2591796.2591803},
  note = {Full version arXiv:1304.8108v1, 2013},
  url = {https://arxiv.org/abs/1304.8108v1}
}

@article{AbdiCornuejolsDadushDalirrooyfard2026,
  author = {Abdi, Ahmad and Cornu{\'e}jols, G{\'e}rard and
            Dadush, Daniel and Dalirrooyfard, Mahsa},
  title = {Lower bounds for cube-ideal set-systems},
  journal = {Proceedings of the London Mathematical Society},
  volume = {133},
  number = {2},
  pages = {e70199},
  year = {2026},
  doi = {10.1112/plms.70199},
  url = {https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/plms.70199}
}

@article{EsperetEtAl2011,
  author = {Esperet, Louis and Kardo{\v{s}}, Franti{\v{s}}ek and
            King, Andrew D. and Kr{\'a}{\v{l}}, Daniel and Norine, Serguei},
  title = {Exponentially Many Perfect Matchings in Cubic Graphs},
  journal = {Advances in Mathematics},
  volume = {227},
  number = {4},
  pages = {1646--1664},
  year = {2011},
  doi = {10.1016/j.aim.2011.03.015},
  url = {https://arxiv.org/abs/1012.2878v2},
  note = {Numbered statements refer to arXiv:1012.2878v2,
          5 September 2011, whose exposition differs from the journal version}
}

@inproceedings{EbrahimnejadEtAl2021,
  author = {Ebrahimnejad, Farzam and Nagda, Ansh and {Oveis Gharan}, Shayan},
  title = {Counting and Sampling Perfect Matchings in Regular Expanding
           Non-Bipartite Graphs},
  booktitle = {13th Innovations in Theoretical Computer Science Conference},
  series = {Leibniz International Proceedings in Informatics},
  volume = {215},
  pages = {61:1--61:12},
  year = {2022},
  doi = {10.4230/LIPIcs.ITCS.2022.61},
  url = {https://arxiv.org/abs/2103.08683v1},
  note = {Conjecture locator refers to arXiv:2103.08683v1, 15 March 2021}
}

@misc{DongJain2026,
  author = {Dong, Dingding and Jain, Vishesh},
  title = {A deterministic {$(1+\varepsilon)^n$} approximation for the
           permanent of a nonnegative matrix},
  year = {2026},
  eprint = {2609.11049},
  archivePrefix = {arXiv},
  note = {Version 1},
  url = {https://arxiv.org/abs/2609.11049v1}
}

@misc{KudriaLuoMajid2026,
  author = {Kudria, Sergei and Luo, Jason and Majid, Mahbod},
  title = {Subexponential Approximation of the Permanent in Deterministic
           Polynomial Time},
  year = {2026},
  eprint = {2609.10516},
  archivePrefix = {arXiv},
  note = {Version 1},
  url = {https://arxiv.org/abs/2609.10516v1}
}

@misc{Yi2026,
  author = {Yi, Zihong},
  title = {Diffuse {Gaussian} Truncation for Deterministic Approximate Counting},
  year = {2026},
  eprint = {2609.04079},
  archivePrefix = {arXiv},
  note = {Version 1},
  url = {https://arxiv.org/abs/2609.04079v1}
}

@inproceedings{SvenssonTarnawski2017,
  author    = {Svensson, Ola and Tarnawski, Jakub},
  title     = {The matching problem in general graphs is in {Quasi-NC}},
  booktitle = {2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)},
  pages     = {696--707},
  publisher = {IEEE},
  year      = {2017},
  doi       = {10.1109/FOCS.2017.70},
  url       = {https://doi.org/10.1109/FOCS.2017.70},
  note      = {Full version: arXiv:1704.01929v2, 4 September 2017}
}




@article{WainwrightJordan2008,
  author = {Wainwright, Martin J. and Jordan, Michael I.},
  title = {Graphical Models, Exponential Families, and Variational Inference},
  journal = {Foundations and Trends in Machine Learning},
  volume = {1}, number = {1--2}, pages = {1--305}, year = {2008},
  doi = {10.1561/2200000001},
  url = {https://doi.org/10.1561/2200000001}
}

@article{ChungGrahamFranklShearer1986,
  author = {Chung, Fan R. K. and Graham, Ronald L. and Frankl, Peter and Shearer, James B.},
  title = {Some Intersection Theorems for Ordered Sets and Graphs},
  journal = {Journal of Combinatorial Theory, Series A},
  volume = {43}, number = {1}, pages = {23--37}, year = {1986},
  doi = {10.1016/0097-3165(86)90019-1},
  url = {https://www.renyi.hu/~pfrankl/j32.pdf}
}




@article{Schrijver1998Counting,
  author  = {Schrijver, Alexander},
  title   = {Counting 1-Factors in Regular Bipartite Graphs},
  journal = {Journal of Combinatorial Theory, Series B},
  year    = {1998},
  volume  = {72},
  number  = {1},
  pages   = {122--135},
  month   = jan,
  doi     = {10.1006/jctb.1997.1798},
  url     = {https://doi.org/10.1006/jctb.1997.1798}
}


@techreport{Gurvits2011SchrijverBethe,
  author      = {Gurvits, Leonid},
  title       = {Unleashing the power of {Schrijver}'s permanental inequality
                 with the help of the {Bethe} Approximation},
  institution = {Electronic Colloquium on Computational Complexity},
  type        = {ECCC Report},
  number      = {TR11-169},
  year        = {2011},
  url         = {https://eccc.weizmann.ac.il/report/2011/169/},
  eprint      = {1106.2844v11},
  archivePrefix = {arXiv},
  primaryClass  = {math.CO},
  note        = {Expanded version: arXiv:1106.2844v11 (20 June 2012)}
}


@article{CyganPilipczukSkrekovski2013,
  author  = {Cygan, Marek and Pilipczuk, Marcin and {\v{S}}krekovski, Riste},
  title   = {A bound on the number of perfect matchings in {Klee}-graphs},
  journal = {Discrete Mathematics \& Theoretical Computer Science},
  year    = {2013},
  volume  = {15},
  number  = {1},
  pages   = {37--52},
  month   = jan,
  doi     = {10.46298/dmtcs.633},
  url     = {https://dmtcs.episciences.org/633},
  issn    = {1365-8050}
}




@article{FordFulkerson1957,
 author={Ford, Jr., L. R. and Fulkerson, D. R.},
 title={A Simple Algorithm for Finding Maximal Network Flows and an Application to the {Hitchcock} Problem},
 journal={Canadian Journal of Mathematics}, volume={9}, pages={210--218}, year={1957},
 doi={10.4153/CJM-1957-024-0}, url={https://doi.org/10.4153/CJM-1957-024-0}
}
@article{Polyak1967,
 author={Polyak, B. T.}, title={A general method for solving extremal problems},
 journal={Doklady Akademii Nauk SSSR}, volume={174}, number={1}, pages={33--36}, year={1967},
 note={In Russian; method citation refers to Equation (1)},
 url={https://www.mathnet.ru/eng/dan33049}
}

@misc{OpenAIMatchingFPRAS2026,
  author = {{OpenAI}},
  title = {{A Fully Polynomial Randomized Approximation Scheme for Perfect Matchings in General Graphs}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/A-Fully-Polynomial-Randomized-Approximation-Scheme-for-Perfect-Matchings-in-General-Graphs-September-23-2026/main.pdf}{OAI:A-Fully-Polynomial-Randomized-Approximation-Scheme-for-Perfect-Matchings-in-General-Graphs-September-23-2026}},
  year = {2026}
}

@article{Naddef1982,
  author = {Naddef, Denis},
  title = {Rank of Maximum Matchings in a Graph},
  journal = {Mathematical Programming},
  volume = {22},
  pages = {52--70},
  year = {1982},
  doi = {10.1007/BF01581025},
  url = {https://doi.org/10.1007/BF01581025}
}

@article{EdmondsPulleyblankLovasz1982,
  author = {Edmonds, Jack and Pulleyblank, William R. and Lov{\'a}sz, L{\'a}szl{\'o}},
  title = {Brick Decompositions and the Matching Rank of Graphs},
  journal = {Combinatorica},
  volume = {2},
  number = {3},
  pages = {247--274},
  year = {1982},
  doi = {10.1007/BF02579233},
  url = {https://doi.org/10.1007/BF02579233}
}
