On the structure of matrices avoiding interval-minor patterns
| Autor: | Jelínek, Vít, Kučera, Stanislav |
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| Rok vydání: | 2018 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 3x3 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 c(P) such that any row and any column in any critical P-avoiding matrix can be partitioned into at most c(P) 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 $n\times n$ having a row with $\Omega(n)$ alternating intervals of 0-entries and 1-entries. Comment: 29 pages, 15 figures |
| Databáze: | arXiv |
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