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arXiv · 1701.07157

Lonesum decomposable matrices

Ken Kamano
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Abstract

A lonesum matrix is a $(0,1)$-matrix that is uniquely determined by its row and column sum vectors. In this paper, we introduce lonesum decomposable matrices and study their properties. We provide a necessary and sufficient condition for a matrix $A$ to be lonesum decomposable, and give a generating function for the number $D_k(m,n)$ of $m\times n$ lonesum decomposable matrices of order $k$. Moreover, by using this generating function we prove some congruences for $D_k(m,n)$ modulo a prime.

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Ken Kamano. 2017-01-25. Lonesum decomposable matrices. https://arxiv.org/abs/1701.07157

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