Let p be a prime, and let L be a set of s congruence classes modulo p. Let $${\mathcal{H}}$$ be a family of subsets of [n] such that the size modulo p of each member of $${\mathcal{H}}$$ is not in L, but the size modulo p of every intersection of k distinct members of $${\mathcal{H}}$$ is in L. We prove that $$|{{\mathcal{H}}}|\le(k-1)\sum_{i=0}^s {n-1\choose i}$$ , improving the bound due to Grolmusz and generalizing results proved for k = 2 by Snevily.
['Weiting Cao', 'Kyung-Won Hwang', 'Douglas B. West']
Improved Bounds on Families Under k -wise Set-Intersection Constraints