On the structure of matrices avoiding interval-minor patterns
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10384805" target="_blank" >RIV/00216208:11320/18:10384805 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.aam.2018.07.005" target="_blank" >https://doi.org/10.1016/j.aam.2018.07.005</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.aam.2018.07.005" target="_blank" >10.1016/j.aam.2018.07.005</a>
Alternative languages
Result language
angličtina
Original language name
On the structure of matrices avoiding interval-minor patterns
Original language description
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 3 x 3 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 cp such that any row and any column in any critical P-avoiding matrix can be partitioned into at most cp 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 x n having a row with Omega(n) alternating intervals of 0-entries and 1-entries.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
<a href="/en/project/GJ16-01602Y" target="_blank" >GJ16-01602Y: Topological and geometric approaches to classes of permutations and graph properties</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Advances in Applied Mathematics
ISSN
0196-8858
e-ISSN
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Volume of the periodical
101
Issue of the periodical within the volume
October 2018
Country of publishing house
US - UNITED STATES
Number of pages
30
Pages from-to
70-99
UT code for WoS article
000447572900004
EID of the result in the Scopus database
2-s2.0-85050459981