On multiple pattern avoiding set partitions

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

On multiple pattern avoiding set partitions

Popis výsledku v původním jazyce

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

Název v anglickém jazyce

On multiple pattern avoiding set partitions

Popis výsledku anglicky

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

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

—

Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2013

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Advances in Applied Mathematics

ISSN

0196-8858

e-ISSN

—

Svazek periodika

50

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

35

Strana od-do

292-326

Kód UT WoS článku

000313922100004

EID výsledku v databázi Scopus

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