On multiple pattern avoiding set partitions
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F13%3A10135347" target="_blank" >RIV/00216208:11320/13:10135347 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.aam.2012.09.002" target="_blank" >http://dx.doi.org/10.1016/j.aam.2012.09.002</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.aam.2012.09.002" target="_blank" >10.1016/j.aam.2012.09.002</a>
Alternative languages
Result language
angličtina
Original language name
On multiple pattern avoiding set partitions
Original language description
We study classes of set partitions determined by the avoidance of multiple patterns, applying a natural notion of partition containment that has been introduced by Sagan. We say that two sets S and T of patterns are equivalent if for each n the number ofpartitions of size n avoiding all the members of S is the same as the number of those that avoid all the members of T. Our goal is to classify the equivalence classes among two-element pattern sets of several general types. First, we focus on pairs of patterns {sigma, tau}, where sigma is a pattern of size three with at least two distinct symbols and tau is an arbitrary pattern of size k that avoids sigma. We show that pattern-pairs of this type determine a small number of equivalence classes; in particular, the classes have on average exponential size in k. We provide a (sub-exponential) upper bound for the number of equivalence classes, and provide an explicit formula for the generating function of all such avoidance classes, showing
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
BA - General mathematics
OECD FORD branch
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Result continuities
Project
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Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2013
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
50
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
35
Pages from-to
292-326
UT code for WoS article
000313922100004
EID of the result in the Scopus database
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