Large B_d-free and Union-free Subfamilies

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F12%3A10108497" target="_blank" >RIV/00216208:11320/12:10108497 - isvavai.cz</a>
Result on the web
<a href="http://epubs.siam.org/sidma/resource/1/sjdmec/v26/i1/p71_s1" target="_blank" >http://epubs.siam.org/sidma/resource/1/sjdmec/v26/i1/p71_s1</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/110823109" target="_blank" >10.1137/110823109</a>

Result language
angličtina
Original language name
Large B_d-free and Union-free Subfamilies
Original language description
Let F be a family of finite sets. A subfamily F' of F is B2-free if it does not contain distinct sets A1,...,A4 such that the union of A1 and A2 is A3 and the intersection of A1 and A2 is A4. Similarly, a subfamily is Bd-free if it does not contain 2^d sets that form a copy of the Boolean lattice Bd. The size of the largest Bd-free subfamily of F will be denoted by f(F,Bd-free), and f(m,Bd-free) will denote the minimum of f(F,Bd-free) over all families F of cardinality m. Instead of ''Bd-free" we can take any other property Gamma, and define f(m,Gamma) analogously. We provide lower and upper bounds for f(m,Bd-free). In particular, we show that f(m,B2-free) is at least cm^{2/3} for a constant c, verifying conjecture by Erdos and Shelah from 1972. We also generalize the notion of union-free families investigated by Erdos and Komlos, Kleitman, and Erdos and Shelah, and prove results about a-union-free families, i.e., families that do not contain distinct sets A1,...,A{a+1} such that the u
Czech name
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Czech description
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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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Project
<a href="/en/project/1M0545" target="_blank" >1M0545: Institute for Theoretical Computer Science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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