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[КНИГА][B] Extremal finite set theory
Extremal Finite Set Theory surveys old and new results in the area of extremal set system
theory. It presents an overview of the main techniques and tools (shifting, the cycle method …
theory. It presents an overview of the main techniques and tools (shifting, the cycle method …
The journey of the union-closed sets conjecture
H Bruhn, O Schaudt - Graphs and Combinatorics, 2015 - Springer
The Journey of the Union-Closed Sets Conjecture | Graphs and Combinatorics Skip to main
content Springer Nature Link Account Menu Find a journal Publish with us Track your research …
content Springer Nature Link Account Menu Find a journal Publish with us Track your research …
Union-closed families of sets
I Balla, B Bollobás, T Eccles - Journal of Combinatorial Theory, Series A, 2013 - Elsevier
A family of sets is union-closed if it contains the union of any two of its elements. Reimer
(2003)[16] and Czédli (2009)[2] investigated the average size of an element of a union …
(2003)[16] and Czédli (2009)[2] investigated the average size of an element of a union …
[HTML][HTML] The graph formulation of the union-closed sets conjecture
H Bruhn, P Charbit, O Schaudt, JA Telle - European Journal of …, 2015 - Elsevier
The union-closed sets conjecture asserts that in a finite non-trivial union-closed family of
sets there has to be an element that belongs to at least half the sets. We show that this is …
sets there has to be an element that belongs to at least half the sets. We show that this is …
[PDF][PDF] The 12 element case of Frankl's conjecture
B Vuckovic, M Zivkovic - preprint, 2012 - researchgate.net
The 12-Element Case of Frankl’s Conjecture Page 1 The 12-Element Case of Frankl’s
Conjecture Vuckovic, Bojan and ˇZivkovic, Miodrag Abstract: According to Frankl’s conjecture …
Conjecture Vuckovic, Bojan and ˇZivkovic, Miodrag Abstract: According to Frankl’s conjecture …
Two results on union-closed families
I Karpas - arxiv preprint arxiv:1708.01434, 2017 - arxiv.org
We show that there is some absolute constant $ c> 0$, such that for any union-closed family
$\mathcal {F}\subseteq 2^{[n]} $, if\mbox {$|\mathcal {F}|\geq (\frac {1}{2}-c) 2^ n $}, then …
$\mathcal {F}\subseteq 2^{[n]} $, if\mbox {$|\mathcal {F}|\geq (\frac {1}{2}-c) 2^ n $}, then …
Frequent elements in union-closed set families
S Das, S Wu - arxiv preprint arxiv:2412.03862, 2024 - arxiv.org
The Union-Closed Sets Conjecture asks whether every union-closed set family $\mathcal {F}
$ has an element contained in $\frac12|\mathcal {F}| $ of its sets. In 2022, Nagel posed a …
$ has an element contained in $\frac12|\mathcal {F}| $ of its sets. In 2022, Nagel posed a …
A Study On The Graph Formulation Of Union Closed Conjecture
J Nived - arxiv preprint arxiv:2409.02221, 2024 - arxiv.org
The Union Closed Conjecture is one of the most renowned problems in Combinatorics. Its
appeal lies in the simplicity of its statement contrasted with the potential complexity of its …
appeal lies in the simplicity of its statement contrasted with the potential complexity of its …
Small sets in union-closed families
D Ellis, MR Ivan, I Leader - arxiv preprint arxiv:2201.11484, 2022 - arxiv.org
Our aim in this note is to show that, for any $\epsilon> 0$, there exists a union-closed family
$\mathcal F $ with (unique) smallest set $ S $ such that no element of $ S $ belongs to more …
$\mathcal F $ with (unique) smallest set $ S $ such that no element of $ S $ belongs to more …
[PDF][PDF] A note on transitive union-closed families
J Aaronson, D Ellis, I Leader - arxiv preprint arxiv:2010.08795, 2020 - arxiv.org
arxiv:2010.08795v3 [math.CO] 6 Dec 2020 Page 1 arxiv:2010.08795v3 [math.CO] 6 Dec 2020
A note on transitive union-closed families. James Aaronson∗, David Ellis† and Imre Leader‡ …
A note on transitive union-closed families. James Aaronson∗, David Ellis† and Imre Leader‡ …