On the Principal Permanent Rank Characteristic Sequences of Graphs and Digraphs

Keivan Hassani Monfared; Paul Horn; Franklin H. J. Kenter; Kathleen Nowak; John Sinkovic; Josh Tobin

paper

On the Principal Permanent Rank Characteristic Sequences of Graphs and Digraphs

arXiv:1510.05153

Abstract

The principal permanent rank characteristic sequence is a binary sequence $r_{0} r_{1} \dots r_{n}$ where $r_{k} = 1$ if there exists a principal square submatrix of size $k$ with nonzero permanent and $r_{k} = 0$ otherwise, and $r_{0} = 1$ if there is a zero diagonal entry. A characterization is provided for all principal permanent rank sequences obtainable by the family of nonnegative matrices as well as the family of nonnegative symmetric matrices. Constructions for all realizable sequences are provided. Results for skew-symmetric matrices are also included.

14 pages, 2 figures