Splittings and Ramsey properties of permutation classes
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10312942" target="_blank" >RIV/00216208:11320/15:10312942 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.aam.2014.10.003" target="_blank" >http://dx.doi.org/10.1016/j.aam.2014.10.003</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.aam.2014.10.003" target="_blank" >10.1016/j.aam.2014.10.003</a>
Alternative languages
Result language
angličtina
Original language name
Splittings and Ramsey properties of permutation classes
Original language description
We say that a permutation p is 'merged' from permutations q and r, if we can color the elements of p red and blue so that the red elements are order-isomorphic to q and the blue ones to r. A 'permutation class' is a set of permutations closed under taking subpermutations. A permutation class C is 'splittable' if it has two proper subclasses A and B such that every element of C can be obtained by merging an element of A with an element of B. Several recent papers use splittability as a tool in deriving enumerative results for specific permutation classes. The goal of this paper is to study splittability systematically. As our main results, we show that if q is a sum-decomposable permutation of order at least four, then the class Av(q) of all q-avoidingpermutations is splittable, while if q is a simple permutation, then Av(q) is unsplittable.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
IN - Informatics
OECD FORD branch
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Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2015
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
63
Issue of the periodical within the volume
February
Country of publishing house
US - UNITED STATES
Number of pages
27
Pages from-to
41-67
UT code for WoS article
000348883100003
EID of the result in the Scopus database
2-s2.0-84919430664