Extension Research of Sperner’s Theorem on Compressed Filters

2021 ◽  
Vol 10 (08) ◽  
pp. 2816-2821
Author(s):  
相芯 刘
Keyword(s):  
Sperner's Theorem

scholarly journals Strong versions of Sperner's theorem

1976 ◽  
Vol 20 (1) ◽  
pp. 80-88 ◽  
Author(s):  
Curtis Greene ◽  
Daniel J Kleitman
Keyword(s):  
Sperner's Theorem

scholarly journals A generalization of Sperner's theorem

1981 ◽  
Vol 31 (4) ◽  
pp. 481-485 ◽  
Author(s):  
D. E. Daykin ◽  
P. Frankl ◽  
C. Greene ◽  
A. J. W. Hilton
Keyword(s):  
Sperner's Theorem ◽  
Lym Inequality ◽  
Families Of Subsets

AbstractSome generalizations of Sperner's theorem and of the LYM inequality are given to the case when A1,… At are t families of subsets of {1,…,m} such that a set in one family does not properly contain a set in another.

scholarly journals On Erdős–Ko–Rado for Random Hypergraphs II

2018 ◽  
Vol 28 (1) ◽  
pp. 61-80 ◽  
Author(s):  
A. HAMM ◽  
J. KAHN
Keyword(s):  
Sperner's Theorem ◽  
Random Hypergraphs

Denote by ${\mathcal H}_k$(n, p) the random k-graph in which each k-subset of {1,. . .,n} is present with probability p, independent of other choices. More or less answering a question of Balogh, Bohman and Mubayi, we show: there is a fixed ε > 0 such that if n = 2k + 1 and p > 1 - ε, then w.h.p. (that is, with probability tending to 1 as k → ∞), ${\mathcal H}_k$(n, p) has the ‘Erdős–Ko–Rado property’. We also mention a similar random version of Sperner's theorem.

scholarly journals Sperner's Theorem and a Problem of Erdős, Katona and Kleitman

2014 ◽  
Vol 24 (4) ◽  
pp. 585-608 ◽  
Author(s):  
SHAGNIK DAS ◽  
WENYING GAN ◽  
BENNY SUDAKOV
Keyword(s):  
Set Theory ◽  
Middle Level ◽  
Extremal Set Theory ◽  
Paper Making ◽  
Sperner's Theorem ◽  
Central Result ◽  
Extremal Set

A central result in extremal set theory is the celebrated theorem of Sperner from 1928, which gives the size of the largest family of subsets of [n] not containing a 2-chain, F1 ⊂ F2. Erdős extended this theorem to determine the largest family without a k-chain, F1 ⊂ F2 ⊂ . . . ⊂ Fk. Erdős and Katona, followed by Kleitman, asked how many chains must appear in families with sizes larger than the corresponding extremal bounds.In 1966, Kleitman resolved this question for 2-chains, showing that the number of such chains is minimized by taking sets as close to the middle level as possible. Moreover, he conjectured the extremal families were the same for k-chains, for all k. In this paper, making the first progress on this problem, we verify Kleitman's conjecture for the families whose size is at most the size of the k + 1 middle levels. We also characterize all extremal configurations.

scholarly journals Sperner's Problem for G-Independent Families

2014 ◽  
Vol 24 (3) ◽  
pp. 528-550
Author(s):  
VICTOR FALGAS-RAVRY
Keyword(s):  
Maximal Antichain ◽  
Independent Edge ◽  
Sperner's Theorem ◽  
Independent Families ◽  
Free Sets

Given a graph G, let Q(G) denote the collection of all independent (edge-free) sets of vertices in G. We consider the problem of determining the size of a largest antichain in Q(G). When G is the edgeless graph, this problem is resolved by Sperner's theorem. In this paper, we focus on the case where G is the path of length n − 1, proving that the size of a maximal antichain is of the same order as the size of a largest layer of Q(G).

scholarly journals Hypergraphs and Sperner's theorem

1973 ◽  
Vol 5 (3) ◽  
pp. 287-289 ◽  
Author(s):  
B. Monjardet
Keyword(s):  
Sperner's Theorem

scholarly journals Infinite Sperner's theorem

2022 ◽  
Vol 187 ◽  
pp. 105558
Author(s):  
Benny Sudakov ◽  
István Tomon ◽  
Adam Zsolt Wagner
Keyword(s):  
Sperner's Theorem
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