Multiply union families in Nn

Frankl, Péter and Shinohara, M. and Tokushige, N. (2016) Multiply union families in Nn. EUROPEAN JOURNAL OF COMBINATORICS, 58. pp. 66-74. ISSN 0195-6698

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Abstract

Let An Nn be an r-wise s-union family, that is, a family of sequences with n components of non-negative integers such that for any r sequences in A the total sum of the maximum of each component in those sequences is at most s. We determine the maximum size of A and its unique extremal configuration provided (i) n is sufficiently large for fixed r and s, or (ii) n = r + 1. © 2016 Elsevier Ltd.

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