Matrices with prescribed row and column sums
Alexander Barvinok
TL;DR
This survey reviews recent advances and open questions regarding the structure, enumeration, and statistical properties of 0-1 and non-negative integer matrices with fixed row and column sums.
Contribution
It compiles recent progress on the enumeration, structure, and probabilistic analysis of matrices with prescribed margins, highlighting open problems and new theoretical insights.
Findings
Cardinality estimates for matrices with fixed margins
Analysis of the structure of random matrices from these sets
Discrete Brunn-Minkowski inequality applications
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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