2-bases of quadruples. Combinatorics Probability & Computing. 2006;15(1-2):131-41. Abstract
2-bases of quadruples
Let Beta(n, <= 4) denote the subsets of [n] := {1, 2,..., n} of at most 4 elements. Suppose that F is a set system with the property that every member of B can be written as a union of (at most) two members of F. (Such an F is called a 2-base of B.) Here we answer a question of Erdos proving that [GRAPHICS] and this bound is best possible for n >= 8.
Two-part and k-Sperner families: New proofs using permutations. Siam Journal on Discrete Mathematics. 2005;19(2):489-500. Abstract
Two-part and k-Sperner families: New proofs using permutations
This is a paper about the beauty of the permutation method. New and shorter proofs are given for the theorem [ P. L. Erd. os and G. O. H. Katona, J. Combin. Theory. Ser. A, 43 ( 1986), pp. 58 – 69; S. Shahriari, Discrete Math., 162 ( 1996), pp. 229 – 238] determining all extremal two-part Sperner families and for the uniqueness of k-Sperner families of maximum size [ P. Erd. os, Bull. Amer. Math. Soc., 51 ( 1945), pp. 898 – 902].
Minimum Matrix Representation Of Closure Operations. Discrete Applied Mathematics. 1985;11(2):115-28.