Supersaturation and stability for forbidden subposet problems
نویسندگان
چکیده
منابع مشابه
Supersaturation and stability for forbidden subposet problems
We address a supersaturation problem in the context of forbidden subposets. A family F of sets is said to contain the poset P if there is an injection i : P → F such that p ≤P q implies i(p) ⊂ i(q). The poset on four elements a, b, c, d with a, b ≤ c, d is called a butterfly. The maximum size of a family F ⊆ 2 that does not contain a butterfly is ( n bn/2c ) + ( n bn/2c+1 ) as proved by De Boni...
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The problem of determining the maximum size La(n, P ) that a P -free subposet of the Boolean lattice Bn can have, attracted the attention of many researchers, but little is known about the induced version of these problems. In this paper we determine the asymptotic behavior of La∗(n, P ), the maximum size that an induced P -free subposet of the Boolean lattice Bn can have for the case when P is...
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We asymptotically determine the size of the largest family F of subsets of {1, . . . , n} not containing a given poset P if the Hasse diagram of P is a tree. This is a qualitative generalization of several known results including Sperner’s theorem. Introduction We say that a poset P is a subposet of a poset P ′ if there is an injective map f : P → P ′ such that a 6P b implies f(a) 6P ′ f(b). A ...
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Let F ⊂ 2[n] be a family of subsets of {1, 2, . . . , n}. For any poset H, we say F is H-free if F does not contain any subposet isomorphic to H. Katona and others have investigated the behavior of La(n,H), which denotes the maximum size of H-free families F ⊂ 2[n]. Here we use a new approach, which is to apply methods from extremal graph theory and probability theory to identify new classes of...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2015
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2015.07.004