Tropical Determinant of Integer Doubly-Stochastic Matrices

Details Tropical Determinant of Integer Doubly-Stochastic Matrices Tropical Determinant of Integer Doubly-Stochastic Matrices

2010-05-18

arxiv.org/abs/1005.3342v1

Linear Algebra and its Applications 436, Issue 5 (2012), 1212-1227

Mathematics

Combinatorics

18 pages

Scientific paper

10.1016/j.laa.2011.07.033

Let D(m,n) be the set of all the integer points in the m-dilate of the Birkhoff polytope of doubly-stochastic n by n matrices. In this paper we find the sharp upper bound on the tropical determinant over the set D(m,n). We define a version of the tropical determinant where the maximum over all the transversals in a matrix is replaced with the minimum and then find the sharp lower bound on thus defined tropical determinant over D(m,n).

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