A short note on doubly substochastic analog of Birkhoff's theorem
Combinatorics
2018-01-08 v1
Abstract
Let B be an n by n doubly substochastic matrix. We show that B can be written as a convex combination of no more than {\sigma}(B)+t subpermutation matrices, where {\sigma}(B) is the number of nonzero elements in B and t is the number of fully indecomposable components of B^{comp}, the minimal doubly stochastic completion of B obtained by a specific way.
Keywords
Cite
@article{arxiv.1801.01232,
title = {A short note on doubly substochastic analog of Birkhoff's theorem},
author = {Lei Cao},
journal= {arXiv preprint arXiv:1801.01232},
year = {2018}
}