@article{CDR2010,
  author  = {Cryan, Mary and Dyer, Martin and Randall, Dana},
  title   = {Approximately Counting Integral Flows and Cell-Bounded
             Contingency Tables},
  journal = {SIAM Journal on Computing},
  volume  = {39},
  number  = {7},
  pages   = {2683--2703},
  year    = {2010},
  doi     = {10.1137/060650544},
  url     = {https://epubs.siam.org/doi/10.1137/060650544},
  note    = {\href{https://doi.org/10.1137/060650544}{doi:10.1137/060650544}.
             Author manuscript:
             \url{https://homepages.inf.ed.ac.uk/mcryan/cdr-sicomp.pdf}}
}

@article{BLP2021,
  author  = {Br{\"a}nd{\'e}n, Petter and Leake, Jonathan and Pak, Igor},
  title   = {Lower bounds for contingency tables via {Lorentzian} polynomials},
  journal = {Israel Journal of Mathematics},
  volume  = {253},
  pages   = {43--90},
  year    = {2023},
  doi     = {10.1007/s11856-022-2364-9},
  url     = {https://link.springer.com/article/10.1007/s11856-022-2364-9},
  note    = {\href{https://doi.org/10.1007/s11856-022-2364-9}
                  {doi:10.1007/s11856-022-2364-9}.
             The author manuscript dated 23 June 2021 is available at
             \url{https://www.math.ucla.edu/~pak/papers/BCT8.pdf}}
}

@article{GJ2023,
  author  = {Guo, Heng and Jerrum, Mark},
  title   = {Counting Vertices of Integral Polytopes Defined by Facets},
  journal = {Discrete \& Computational Geometry},
  volume  = {70},
  number  = {3},
  pages   = {975--990},
  year    = {2023},
  doi     = {10.1007/s00454-022-00406-8},
  url     = {https://link.springer.com/article/10.1007/s00454-022-00406-8},
  note    = {\href{https://doi.org/10.1007/s00454-022-00406-8}
                  {doi:10.1007/s00454-022-00406-8}}
}

@article{Barvinok2009,
  author = {Barvinok, Alexander},
  title = {Asymptotic estimates for the number of contingency tables,
           integer flows, and volumes of transportation polytopes},
  journal = {International Mathematics Research Notices},
  volume = {2009},
  number = {2},
  pages = {348--385},
  year = {2009},
  doi = {10.1093/imrn/rnn133},
  note = {\href{https://doi.org/10.1093/imrn/rnn133}{doi:10.1093/imrn/rnn133}}
}

@article{BLSY2010,
  author = {Barvinok, Alexander and Luria, Zur and
            Samorodnitsky, Alex and Yong, Alexander},
  title = {An approximation algorithm for counting contingency tables},
  journal = {Random Structures \& Algorithms},
  volume = {37},
  number = {1},
  pages = {25--66},
  year = {2010},
  doi = {10.1002/rsa.20301},
  note = {\href{https://doi.org/10.1002/rsa.20301}{doi:10.1002/rsa.20301}}
}

@article{JSV2004,
  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},
  note = {\href{https://doi.org/10.1145/1008731.1008738}
          {doi:10.1145/1008731.1008738}}
}

@article{BH2020,
  author = {Br{\"a}nd{\'e}n, Petter and Huh, June},
  title = {Lorentzian polynomials},
  journal = {Annals of Mathematics},
  series = {2},
  volume = {192},
  number = {3},
  pages = {821--891},
  year = {2020},
  doi = {10.4007/annals.2020.192.3.4},
  note = {\href{https://doi.org/10.4007/annals.2020.192.3.4}
          {doi:10.4007/annals.2020.192.3.4}}
}

@misc{AF2002,
  author = {Aldous, David and Fill, James Allen},
  title = {Reversible {Markov} Chains and Random Walks on Graphs},
  year = {2002},
  note = {Unfinished monograph, recompiled 2014.
          \url{https://www.stat.berkeley.edu/~aldous/RWG/book.html}}
}

@article{EK1972,
  author = {Edmonds, Jack and Karp, Richard M.},
  title = {Theoretical Improvements in Algorithmic Efficiency for
           Network Flow Problems},
  journal = {Journal of the ACM},
  volume = {19},
  number = {2},
  pages = {248--264},
  year = {1972},
  note = {\href{https://raw.githubusercontent.com/deltadbu/UCAS_algorithm_course/master/Lectures/EdmondsKarp1972.pdf}
          {Published article}}
}

@article{DKM1997,
  author = {Dyer, Martin and Kannan, Ravi and Mount, John},
  title = {Sampling contingency tables},
  journal = {Random Structures \& Algorithms},
  volume = {10},
  number = {4},
  pages = {487--506},
  year = {1997},
  note = {\url{https://www.math.cmu.edu/~af1p/Teaching/MCC17/Papers/contingency.pdf}}
}

@article{Morris2002,
  author = {Morris, Ben},
  title = {Improved bounds for sampling contingency tables},
  journal = {Random Structures \& Algorithms},
  volume = {21},
  number = {2},
  pages = {135--146},
  year = {2002},
  doi = {10.1002/rsa.10049},
  note = {\href{https://doi.org/10.1002/rsa.10049}{doi:10.1002/rsa.10049}}
}

@article{Prekopa1973,
  author = {Pr{\'e}kopa, Andr{\'a}s},
  title = {On logarithmic concave measures and functions},
  journal = {Acta Scientiarum Mathematicarum (Szeged)},
  volume = {34},
  pages = {335--343},
  year = {1973},
  note = {\url{https://rutcor.rutgers.edu/Prekopa/pdf/SCIENT2.pdf}}
}

@article{Leindler1972,
  author = {Leindler, L{\'a}szl{\'o}},
  title = {On a certain converse of {H\"older}'s inequality. {II}},
  journal = {Acta Scientiarum Mathematicarum},
  volume = {33},
  number = {3--4},
  pages = {217--223},
  year = {1972},
  note = {\url{https://acta.bibl.u-szeged.hu/14358/}}
}

@misc{OpenAICommonBases2026,
  author = {{OpenAI}},
  title = {{Approximate counting of common bases of two matroids}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Approximate-counting-of-common-bases-of-two-matroids-September-23-2026/main.pdf}{OAI:Approximate-counting-of-common-bases-of-two-matroids-September-23-2026}},
  year = {2026}
}

@incollection{DG1995,
  author = {Diaconis, Persi and Gangolli, Anil},
  title = {Rectangular Arrays with Fixed Margins},
  booktitle = {Discrete Probability and Algorithms},
  editor = {Aldous, David and Diaconis, Persi and Spencer, Joel and Steele, J. Michael},
  series = {The IMA Volumes in Mathematics and its Applications},
  volume = {72},
  publisher = {Springer},
  address = {New York},
  pages = {15--41},
  year = {1995},
  doi = {10.1007/978-1-4612-0801-3_3},
  note = {\href{https://doi.org/10.1007/978-1-4612-0801-3_3}
          {doi:10.1007/978-1-4612-0801-3\_3}}
}

@article{DG2000,
  author = {Dyer, Martin and Greenhill, Catherine},
  title = {Polynomial-time counting and sampling of two-rowed contingency tables},
  journal = {Theoretical Computer Science},
  volume = {246},
  number = {1--2},
  pages = {265--278},
  year = {2000},
  doi = {10.1016/S0304-3975(99)00136-X},
  note = {\href{https://doi.org/10.1016/S0304-3975(99)00136-X}
          {doi:10.1016/S0304-3975(99)00136-X}}
}

@article{CD2003,
  author = {Cryan, Mary and Dyer, Martin},
  title = {A polynomial-time algorithm to approximately count contingency tables
           when the number of rows is constant},
  journal = {Journal of Computer and System Sciences},
  volume = {67},
  number = {2},
  pages = {291--310},
  year = {2003},
  doi = {10.1016/S0022-0000(03)00014-X},
  note = {\href{https://doi.org/10.1016/S0022-0000(03)00014-X}
          {doi:10.1016/S0022-0000(03)00014-X}}
}

@inproceedings{Dyer2003,
  author = {Dyer, Martin},
  title = {Approximate counting by dynamic programming},
  booktitle = {Proceedings of the Thirty-Fifth Annual ACM Symposium on Theory of Computing},
  pages = {693--699},
  publisher = {ACM},
  year = {2003},
  doi = {10.1145/780542.780643},
  note = {\href{https://doi.org/10.1145/780542.780643}{doi:10.1145/780542.780643}}
}

@article{JVV1986,
  author = {Jerrum, Mark R. and Valiant, Leslie G. and Vazirani, Vijay V.},
  title = {Random generation of combinatorial structures from a uniform distribution},
  journal = {Theoretical Computer Science},
  volume = {43},
  pages = {169--188},
  year = {1986},
  doi = {10.1016/0304-3975(86)90174-X},
  note = {\href{https://doi.org/10.1016/0304-3975(86)90174-X}
          {doi:10.1016/0304-3975(86)90174-X}}
}

@misc{CVY2026,
  author = {Chen, Xiaoyu and Vigoda, Eric and Yang, Xiongxin},
  title = {Faster {FPRAS} for the Permanent via Restricted {Poincar\'e}
           Inequalities and Coupled Flows},
  year = {2026},
  eprint = {2608.26599},
  archivePrefix = {arXiv},
  primaryClass = {cs.DM},
  note = {Preprint, August 27, 2026.
          \href{https://arxiv.org/abs/2608.26599v1}{arXiv:2608.26599v1}}
}

@misc{OpenAIExactTables2026,
  author = {{OpenAI}},
  title = {{Exact Uniform Sampling of Contingency Tables with Arbitrary Margins}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Exact-Uniform-Sampling-of-Contingency-Tables-with-Arbitrary-Margins-September-24-2026/main.pdf}{OAI:Exact-Uniform-Sampling-of-Contingency-Tables-with-Arbitrary-Margins-September-24-2026}},
  year = {2026}
}

@article{BBV2007,
  author = {Bez{\'a}kov{\'a}, Ivona and Bhatnagar, Nayantara and Vigoda, Eric},
  title = {Sampling binary contingency tables with a greedy start},
  journal = {Random Structures \& Algorithms},
  volume = {30},
  number = {1--2},
  pages = {168--205},
  year = {2007},
  doi = {10.1002/rsa.20155},
  note = {\href{https://doi.org/10.1002/rsa.20155}{doi:10.1002/rsa.20155}}
}

@inproceedings{GKM2011,
  author = {Gopalan, Parikshit and Klivans, Adam and Meka, Raghu and
            {\v{S}}tefankovi{\v{c}}, Daniel and Vempala, Santosh and Vigoda, Eric},
  title = {An {FPTAS} for {\#Knapsack} and Related Counting Problems},
  booktitle = {Proceedings of the 52nd Annual IEEE Symposium on
               Foundations of Computer Science},
  pages = {817--826},
  publisher = {IEEE},
  year = {2011},
  doi = {10.1109/FOCS.2011.32},
  note = {\href{https://doi.org/10.1109/FOCS.2011.32}{doi:10.1109/FOCS.2011.32}.
          Author manuscript:
          \url{https://www.microsoft.com/en-us/research/wp-content/uploads/2016/02/Knapsack-FOCS-final.pdf}}
}

@misc{LMY2026,
  author = {Leake, Jonathan and Mohammadi Yekta, Maryam},
  title = {Log-concavity and Approximate Counting for Totally Unimodular Polytopes},
  year = {2026},
  eprint = {2609.39917},
  archivePrefix = {arXiv},
  primaryClass = {math.CO},
  note = {Preprint, September 30, 2026.
          \href{https://arxiv.org/abs/2609.39917v1}{arXiv:2609.39917v1}}
}
