Combinatorics: set systems, hypergraphs, families of vectors, and combinatorial probability
Combinatorics: set systems, hypergraphs, families of vectors, and combinatorial probability
A general 4-words inequality with consequences for 2-way communication complexity
Advances in Applied Mathematics
Quantum vs. classical communication and computation
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Approximating the independence number via the j -function
Mathematical Programming: Series A and B
The Lovász Theta Function and a Semidefinite Programming Relaxation of Vertex Cover
SIAM Journal on Discrete Mathematics
Set Systems with Restricted Cross-Intersections and the Minimum Rank of Inclusion Matrices
SIAM Journal on Discrete Mathematics
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Suppose A and B are families of subsets of an n-element set and L is a set of s numbers. We say that the pair (A, B) is L-cross-intersecting if |A ∩ B| ∈ L for every A ∈ A and B ∈ B. Among such pairs (A,B) we write PL(n) for the maximum possible value of |A||B|. In this paper we find an exact bound for PL(n) when n is sufficiently large, improving earlier work of Sgall. We also determine P{2}(n) and P{1, 2}(n) exactly, which respectively confirm special cases of a conjecture of Ahlswede, Cai and Zhang and a conjecture of Sgall.