Large B_d-free and union-free subfamilies

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F11%3A10108511" target="_blank" >RIV/00216208:11320/11:10108511 - isvavai.cz</a>

Výsledek na webu

<a href="http://www.sciencedirect.com/science/article/pii/S1571065311000862" target="_blank" >http://www.sciencedirect.com/science/article/pii/S1571065311000862</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.endm.2011.09.017" target="_blank" >10.1016/j.endm.2011.09.017</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Large B_d-free and union-free subfamilies

Popis výsledku v původním jazyce

For a property Gamma and a family of sets F, let f(F,Gamma) be the size of the largest subfamily of F having property Gamma. For a positive integer m, let f(m,Gamma) be the minimum of f(F,Gamma) over all families of size m. A family F is said to be Bd-free if it has no subfamily F'={FI:I is a subset of [d]} of d2 distinct sets such that for every two subsets I,J of [d], the union of FI and FJ is euqal to F(I union J) and the intersection of FI and FJ is euqal to F(I intersection J). A family F is a-union free if the union of F_1, F_2... and F_a is different from F_a+1 whenever F1,...,F_a+1 are distinct sets in F. We verify a conjecture of Erdős and Shelah that f(m,B2-free)=Theta(m2/3). We also obtain lower and upper bounds for f(m,Bd-free) and f(m,a-union free).

Název v anglickém jazyce

Large B_d-free and union-free subfamilies

Popis výsledku anglicky

For a property Gamma and a family of sets F, let f(F,Gamma) be the size of the largest subfamily of F having property Gamma. For a positive integer m, let f(m,Gamma) be the minimum of f(F,Gamma) over all families of size m. A family F is said to be Bd-free if it has no subfamily F'={FI:I is a subset of [d]} of d2 distinct sets such that for every two subsets I,J of [d], the union of FI and FJ is euqal to F(I union J) and the intersection of FI and FJ is euqal to F(I intersection J). A family F is a-union free if the union of F_1, F_2... and F_a is different from F_a+1 whenever F1,...,F_a+1 are distinct sets in F. We verify a conjecture of Erdős and Shelah that f(m,B2-free)=Theta(m2/3). We also obtain lower and upper bounds for f(m,Bd-free) and f(m,a-union free).

Druh

O - Ostatní výsledky

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/1M0545" target="_blank" >1M0545: Institut Teoretické Informatiky</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2011

Kód důvěrnosti údajů

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