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We give a deterministic polynomial time $2^{O(r)}$-approximation algorithm for the number of bases of a given matroid of rank $r$ and the number of common bases of any two matroids of rank $r$.
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William Cunningham · 1984
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“Elementary bounds on Poincaré and log-Sobolev constants for decomposable Markov chains”
Mark Jerrum, Jung-Bae Son, Prasad Tetali and Eric Vigoda · 2004
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“A Polynomial-time Approximation Algorithm for the Permanent of a Matrix with Nonnegative Entries”
Mark Jerrum, Alistair Sinclair and Eric Vigoda · 2004
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Leonid Gurvits and Alex Samorodnitsky · 2014
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Mohit Singh and Nisheeth. Vishnoi · 2014
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“Lattice Path Matroids: Negative Correlation and Fast Mixing”, 2015
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”
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Alexander Barvinok and Alex Samorodnitsky · 2007
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Leonid Gurvits · 2008
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“Approximating the Number of Bases for Almost All Matroids”
Brian. Cloteaux · 2010
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“Counting bases of representable matroids”
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“Matrix analysis”
Roger. Horn and Charles. Johnson · 2013
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Aleksandar Nikolov and Mohit Singh · 2016
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June Huh and Botong Wang · 2017
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Damian Straszak and Nisheeth. Vishnoi · 2017
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