TY - GEN

T1 - Disjoint systems

AU - Alon, Noga Mordechai

AU - Sudakov, Benny

PY - 1994/1/1

Y1 - 1994/1/1

N2 - A disjoint system of type (∀, ∃, k, n) is a collection C={A1, …, Am} of pairwise disjoint families of k-subsets of an n-element set satisfying the following condition. For every ordered pair Ai and Aj of distinct members of C and for every A ∈ Ai there exists a B ∈ Aj that does not intersect A. Let Dn(∀, ∃, k) denote the maximum possible cardinality of a disjoint system of type (∀, ∃, k, n). It is shown that for every fixed k≥2, (Formula Presented) This settles a problem of Ahlswede, Cai and Zhang. Several related problems are considered as well.

AB - A disjoint system of type (∀, ∃, k, n) is a collection C={A1, …, Am} of pairwise disjoint families of k-subsets of an n-element set satisfying the following condition. For every ordered pair Ai and Aj of distinct members of C and for every A ∈ Ai there exists a B ∈ Aj that does not intersect A. Let Dn(∀, ∃, k) denote the maximum possible cardinality of a disjoint system of type (∀, ∃, k, n). It is shown that for every fixed k≥2, (Formula Presented) This settles a problem of Ahlswede, Cai and Zhang. Several related problems are considered as well.

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M3 - Conference contribution

AN - SCOPUS:85026852518

SN - 9783540578437

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 159

EP - 163

BT - Algebraic Coding - 1st French-Israeli Workshop, Proceedings

PB - Springer Verlag

T2 - 1st French-Israeli Workshop on Algebraic Coding, 1993

Y2 - 19 July 1993 through 21 July 1993

ER -