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
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.
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