An exact characterization of saturation for permutation matrices

Abstract

A 0-1 matrix $M$ contains a 0-1 matrix pattern $P$ if we can obtain $P$ from $M$ by deleting rows and/or columns and turning arbitrary 1-entries into 0s. The saturation function $\mathrm{sat}(P,n)$ for a 0-1 matrix pattern $P$ indicates the minimum number of 1s in an $n\times n$ 0-1 matrix that does not contain $P$, but changing any 0-entry into a 1-entry creates an occurrence of $P$. Fulek and Keszegh recently showed that each pattern has a saturation function either in $O(1)$ or in $\Theta (n)$. We fully classify the saturation functions of permutation matrices.

Revised journal version, as published in Combinatorial Theory. Supersedes arXiv:2012.14717, with text overlap

References in corpus (3)

• Small permutation classes
• Pattern-Avoiding (0,1)-Matrices
• Matrix patterns with bounded saturation function

Cited by in corpus (1)

• Sequence saturation