A family A of ‘-element subsets and a family B of k-element subsets of an n-element set are cross-intersecting if every set from A has a nonempty intersection with every set from B. We compare two… (More)

For a Sperner family A ⊆ 2 [n] let Ai denote the family of all i-element sets in A. We sharpen the LYM inequality i |Ai|/ n i ≤ 1 by adding to the LHS all possible products of fractions |Ai|/ n i ,… (More)

A weight function ! : 2 → R¿0 from the set of all subsets of [n]={1; : : : ; n} to the nonnegative real numbers is called shift-monotone in {m+1; : : : ; n} if !({a1; : : : ; aj})¿!({b1; : : : ; bj})… (More)

We determine lattice polytopes of smallest volume with a given number of interior lattice points. We show that the Ehrhart polynomials of those with one interior lattice point have largest roots with… (More)

, I≤k(n, t) = I (n, t) ∩ 2 ( [n] ≤k ) . After the maximal families inI (n, t) [13] and in Ik(n, t) [1, 9] are known we study now maximal families in I≤k(n, t). We present a conjecture about the… (More)

Minkowski’s second theorem on successive minima gives an upper bound on the volume of a convex body in terms of its successive minima. We study the problem to generalize Minkowski’s bound by… (More)

We show that the average size of subsets of [n] forming an intersecting Sperner family of cardinality not less than ( n−1 k−1 ) is at least k provided that k6 n=2− √ n=2 + 1. The statement is not… (More)