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 …

This is a paper about the beauty of the permutation method. New and shorter proofs are
given for the theorem [PL Erdos and GOH Katona, J. Combin. Theory. Ser. A, 43 (1986), pp …

In this paper we investigate common generalizations of more-part and L-Sperner families.
We prove a BLYM inequality for M-part L-Sperner families and obtain results regarding the …

All Maximum Size Two-Part Sperner Systems: In Short Page 1 Combinatorics, Probability and
Computing (2007) 16, 553–555. c 2007 Cambridge University Press doi:10.1017/S0963548306007930 …

Конечное упорядоченное множество называется шпернеровым, если среди его
максимальных по длине антицепей хотя бы одна составлена из элементов одинаковой …

Let 2 [n] denote the poset of all subsets of [n]={1, 2,..., n} ordered by inclusion. Following
Gutterman and Shahriari (Order 14, 1998, 321–325) we consider a game G n (a, b, c). This …

In the Boolean lattice the BLYM inequality holds with equality if and only if the Sperner family
consists of one complete level of subsets. In this paper we extend this strict BLYM-property …

Let F be a family of distinct subsets of an n-element set. Define pi (F)(0⩽ i⩽ n) as the number
of i-element members of F. Consider the profile vectors (p0 (F),…, pn (F)) for all families F …

The authors present several neat applications of the permutation method to show Sperner
type inequalities, focusing especially on the cases for which equality holds. They give two …