Diagonal Sums of Doubly Stochastic Matrices

2021/01/11 by Brualdi, Richard A., Dahl, Geir · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2101.04143

Abstract

Let Ω_n denote the class of n × n doubly stochastic matrices (each such matrix is entrywise nonnegative and every row and column sum is 1). We study the diagonals of matrices in Ω_n. The main question is: which A ∈ Ω_n are such that the diagonals in A that avoid the zeros of A all have the same sum of their entries. We give a characterization of such matrices, and establish several classes of patterns of such matrices.

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