Cookies?
Library Header Image
LSE Research Online LSE Library Services

On the structure of matrices avoiding interval-minor patterns

Jelínek, Vít and Kucera, Stanislav (2018) On the structure of matrices avoiding interval-minor patterns. Advances in Applied Mathematics, 101. pp. 70-99. ISSN 0196-8858

[img] Text - Accepted Version
Restricted to Repository staff only until 27 July 2019.

Download (1MB) | Request a copy
Identification Number: 10.1016/j.aam.2018.07.005

Abstract

We study the structure of 01-matrices avoiding a pattern P as an interval minor. We focus on critical P-avoiders, i.e., on the P-avoiding matrices in which changing a 0-entry to a 1-entry always creates a copy of P as an interval minor. Let Q be the permutation matrix corresponding to the permutation 231. As our main result, we show that for every pattern P that has no rotated copy of Q as interval minor, there is a constant such that any row and any column in any critical P-avoiding matrix can be partitioned into at most intervals, each consisting entirely of 0-entries or entirely of 1-entries. In contrast, for any pattern P that contains a rotated copy of Q, we construct critical P-avoiding matrices of arbitrary size having a row with alternating intervals of 0-entries and 1-entries.

Item Type: Article
Official URL: https://www.sciencedirect.com/journal/advances-in-...
Additional Information: © 2018 Elsevier Inc.
Subjects: Q Science > QA Mathematics
Sets: Departments > Mathematics
Date Deposited: 14 Aug 2018 14:33
Last Modified: 18 Oct 2018 15:19
Projects: 16-01602Y
Funders: Czech Science Foundation, Neuron Foundation for the Support of Science
URI: http://eprints.lse.ac.uk/id/eprint/89854

Actions (login required)

View Item View Item

Downloads

Downloads per month over past year

View more statistics