Chvátal's conjecture and correlation inequalities
نویسندگان
چکیده
Chvátal’s conjecture in extremal combinatorics asserts that for any decreasing family F of subsets of a finite set S, there is a largest intersecting subfamily of F consisting of all members of F that include a particular x ∈ S. In this paper we reformulate the conjecture in terms of influences of variables on Boolean functions and correlation inequalities, and study special cases and variants using tools from discrete Fourier analysis.
منابع مشابه
On Chvátal's conjecture and a conjecture on families of signed sets
A family H of sets is said to be hereditary if all subsets of any set in H are in H; in other words, H is hereditary if it is a union of power sets. A family A is said to be intersecting if no two sets in A are disjoint. A star is a family whose sets contain at least one common element. An outstanding open conjecture due to Chvátal claims that among the largest intersecting sub-families of any ...
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Using Kleitman’s lemma and results of Sch2 onheim and Mikl os it is shown that if w(D)= |D|=2, then every maximum-sized intersecting family in D contains all base elements of D. Then, the converse of this statement is conjectured and shown that this is equivalent to that of Chv atal. c © 2002 Elsevier Science B.V. All rights reserved.
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ورودعنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 156 شماره
صفحات -
تاریخ انتشار 2018