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We give new lower and upper bounds on the permanent of a doubly stochastic matrix.
Heilmann, Ole J.; Lieb, Elliott H. Theory of monomer-dimer systems
1972
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1973
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1980
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D. I. Falikman, Proof of the van der Waerden’s conjecture on the permanent of a doubly stochastic matrix
1981
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S. Friedland, A proof of a generalized van der Waerden conjecture on permanents
1982
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L. Lovasz and M. D. Plummer, Matching Theory
1986
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A. Z. Broder, How hard is it to marry at random? (On the approximation of the permanent)
1988
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A. Schrijver, Counting 1-factors in regular bipartite graphs
1998
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A. I. Barvinok, Polynomial Time Algorithms to Approximate Permanents and Mixed Discriminants Within a Simply Exponential Factor
1999
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N. Linial, A. Samorodnitsky, A.Wigderson, A Deterministic Strongly Polynomial Algorithm for Matrix Scaling and Approximate Permanents
2000
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A. Zygmund, Trigonometric series
2002
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G. W. Soules, New permanental upper bounds for nonnegative matrices
2008
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S. Friedland and L. Gurvits, Lower Bounds for Partial Matchings in Regular Bipartite Graphs and Applications to the Monomer-Dimer Entropy
2008
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L. Gurvits, Van der Waerden/Schrijver-Valiant like conjectures and stable (aka hyperbolic) homogeneous polynomials: one theorem for all
2008
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A. Samorodnitsky, An upper bound for permanents of nonnegative matrices
2008
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L. Gurvits, A polynomial-time algorithm to approximate the mixed volume within a simply exponential factor
2009
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2003
Cited alongside, same era.
M. Jerrum, A. Sinclair, and E. Vigoda, A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries
2004
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S. Friedland, E. Krop, P. H. Lundow, K. Markström, Validations of the Asymptotic Matching Conjectures
2006
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B. Huang and T. Jebara, Approximating the Permanent with Belief Propagation
2007
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A. Ferber, M. Krivelevich and B. Sudakov, Counting and packing Hamilton cycles in dense graphs and oriented graphs
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M. Laurent, A. Schrijver, On Leonid Gurvits’s proof for permanents
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A. Wigderson, personal communication
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P.O. Vontobel, The Bethe permanent of a non-negative matrix
2010
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2013
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M. Rudelson, O. Zeitouni, Singular values of Gaussian matrices and permanent estimators
2013
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