LYM-type inequality for t-intersecting antichains in linear lattices
نویسندگان
چکیده
منابع مشابه
Sharpening the LYM inequality
More detailed information about the s t ructure of Sperner families can be obtained by considering their level sequences. The level sequence of a family 4 , f ( ~ ) = {fi(Y)}, has f i (~) equal to the number of members of ~ with exac t ly ' / e l emen t s . Sperner 's theorem asserts tha t ~fi(2~)<_ ([~j) . A stronger restriction on the level i sequence was proved independent ly by Lubell, Yama...
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15 صفحه اولA probabilistic proof for the lym-inequality
Here we give a short, inductive argument yielding (1). First note that (1) is evident if n = 1, and also if X E S (in the latter case necessarily 9 -= 1.x) holds). Now assume (1) is true for n 1, !F is an antichain and X 4 9. Let x be a random variable which takes the values 1,. . . , n; each with probability l/n. Let us define s(x) = {FE ZF: x9! fl. For any function g(x), we denote by E(g(x)) ...
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Generalizing a result of Miyakawa, Nozaki, Pogosyan and Rosenberg, we prove that there is a one-to-one correspondence between the set of intersecting antichains in a subset of the lower half of the kvalued n-cube and the set of intersecting antichains in the k-valued (n− 1)-cube.
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ژورنال
عنوان ژورنال: SCIENTIA SINICA Mathematica
سال: 2015
ISSN: 1674-7216
DOI: 10.1360/n012015-00064