Mathematics Faculty Articles

Title

Pattern-avoiding (0,1)-matrices and bases of permutation matrices

Document Type

Article

Publication Date

8-4-2021

Publication Title

Discrete Applied Mathematics

Keywords

Permutation, Pattern-avoiding, pqr-avoiding, (0, 1)-matrices, Permutation bases

ISSN

0166-218X

Volume

304

First Page

196

Last Page

211

Abstract

We investigate pattern-avoiding n × n (0, 1)-matrices with emphasis on patterns of length 3: pqr-avoiding where {p, q, r} ⊆ {1, 2, . . . , n}. We show that all such maximal (0, 1)-matrices contain the same number of 1’s, and their structure is determined. We then show that the set of pqr-avoiding n × n permutation matrices span the linear space of dimension (n − 1)2 + 1 generated by the n × n permutation matrices and determine a corresponding basis for each p, q, r.

ORCID ID

0000-0001-7613-7191

ResearcherID

G-7341-2019

DOI

10.1016/j.dam.2021.07.039

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