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We design an FPRAS to count the number of bases of any matroid given by an independent set oracle, and to estimate the partition function of the random cluster model of any matroid in the regime where $0<q<1$.
“The complexity of computing the sign of the Tutte polynomial”
L.. Goldberg and M. Jerrum · 1952
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“On the random-cluster model”, 1971
Cornelis Fortuin · 1971
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“On the random-cluster model: I. Introduction and relation to other models”
Cornelis Fortuin and Pieter Kasteleyn · 1972
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“On the random-cluster model: II. The percolation model”
Cornelis Fortuin · 1972
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“On the random-cluster model: III. The simple random-cluster model”
Cornelis Fortuin · 1972
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“p-adic curvature and the cohomology of discrete subgroups of p-adic groups”
H. Garland · 1973
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“Isoperimetric inequalities for graphs, and superconcentrators”
N. Alon and V. Milman · 1985
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N Alon · 1986
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“Random Generation of Combinatorial Structures from a Uniform Distribution”
Mark Jerrum, Leslie Valiant and Vijay Vazirani · 1986
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“On the expansion of 0/1 polytopes”
M. Mihail and U. Vazirani · 1989
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“On the computational complexity of the Jones and Tutte polynomials”
F. Jaeger, D.. Vertigan and D… Welsh · 1990
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“Geometric bounds for eigenvalues of Markov chains”
Persi Diaconis and Daniel Stroock · 1991
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“Connectivity Properties of Matroids”, 1991
Milena Mihail and Madhu Sudan · 1991
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“On the computational complexity of tutte, jones, homfly and kauffman invariants”, 1991
D.L. Vertigan · 1991
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“Balanced matroids”
Tomás Feder and Milena Mihail · 1992
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“Polynomial-time approximation algorithms for the Ising model”
Mark Jerrum and Alistair Sinclair · 1993
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“The computational complexity of knot and matroid polynomials”
D.J.A Welsh · 1994
Cited alongside, same era.
“On L2-cohomology and property (T) for automorphism groups of polyhedral cell complexes”
W. Ballmann and J. Światkowski · 1997
Cited alongside, same era.
“On approximating the number of bases of exchange preserving matroids”
Anna Gambin · 1999
Cited alongside, same era.
“Spectral gap and log-Sobolev constant for balanced matroids”
Mark Jerrum and Jung Son · 2002
Cited alongside, same era.
“Elementary bounds on Poincaré and log-Sobolev constants for decomposable Markov chains”
Mark Jerrum, Jung-Bae Son, Prasad Tetali and Eric Vigoda · 2004
Cited alongside, same era.
“Two Remarks Concerning Balanced Matroids”
Mark Jerrum · 2006
Cited alongside, same era.
“Approximating the Tutte polynomial of a binary matroid and other related combinatorial polynomials”
L.. Goldberg and M. Jerrum · 2013
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“Matrix analysis”
Roger Horn and Charles Johnson · 2013
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“Lattice path matroids: negative correlation and fast mixing”
Emma Cohen, Prasad Tetali and Damir Yeliussizov · 2015
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“Monte Carlo Markov Chain Algorithms for Sampling Strongly Rayleigh Distributions and Determinantal Point Processes”
Nima Anari, Shayan Oveis Gharan and Alireza Rezaei · 2016
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“Enumeration of points, lines, planes, etc”
June Huh and Botong Wang · 2016
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“Random weighting, asymptotic counting, and inverse isoperimetry”
Alexander Barvinok and Alex Samorodnitsky · 2007
Cited alongside, same era.
“Inapproximability of the Tutte polynomial”
L.. Goldberg and M. Jerrum · 2008
Cited alongside, same era.
“The Random-Cluster Model”
G. Grimmett · 2009
Cited alongside, same era.
“A polynomial-time algorithm to approximate the mixed volume within a simply exponential factor”
Leonid Gurvits · 2009
Cited alongside, same era.
“Approximating the Number of Bases for Almost All Matroids”
Brian. Cloteaux · 2010
Cited alongside, same era.
“On multivariate Newton-like inequalities”
Leonid Gurvits · 2010
Cited alongside, same era.
“High Dimensional Expanders Imply Agreement Expanders”
I. Dinur and T. Kaufman · 2017
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“Random cluster dynamics for the Ising model is rapidly mixing”
Heng Guo and Mark Jerrum · 2017
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“High Dimensional Random Walks and Colorful Expansion”
Tali Kaufman and David Mass · 2017
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“High Dimensional Expanders”, 2017
Alexander Lubotzky · 2017
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“Hodge theory for combinatorial geometries”
Karim Adiprasito, June Huh and Eric Katz · 2018
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Nima Anari, Shayan Oveis Gharan and Cynthia Vinzant · 2018
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