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

On the Principal Permanent Rank Characteristic Sequences of Graphs and Digraphs

Combinatorics 2015-10-20 v1

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

Abstract

The principal permanent rank characteristic sequence is a binary sequence $r_0 r_1 \ldots r_n$ 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.

Keywords

principal permanent rank characteristic sequence graphs digraphs nonnegative matrices symmetric matrices skew-symmetric matrices

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@article{arxiv.1510.05153,
  title  = {On the Principal Permanent Rank Characteristic Sequences of Graphs and Digraphs},
  author = {Keivan Hassani Monfared and Paul Horn and Franklin H. J. Kenter and Kathleen Nowak and John Sinkovic and Josh Tobin},
  journal= {arXiv preprint arXiv:1510.05153},
  year   = {2015}
}

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14 pages, 2 figures

On the Principal Permanent Rank Characteristic Sequences of Graphs and Digraphs

Abstract

Keywords

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