Matrices with prescribed row and column sums

2010/10/27 by Barvinok, Alexander
#05A16 #05C30 #05C50 #15B34 #15B36 #60C05 #60F05 #60F10 #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1010.5706

Abstract

This is a survey of the recent progress and open questions on the structure of the sets of 0-1 and non-negative integer matrices with prescribed row and column sums. We discuss cardinality estimates, the structure of a random matrix from the set, discrete versions of the Brunn-Minkowski inequality and the statistical dependence between row and column sums.

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