A Note on Set Systems with no Union of Cardinality 0 Modulo m
نویسنده
چکیده
Alon, Kleitman, Lipton, Meshulam, Rabin and Spencer (Graphs. Combin. 7 (1991), no. 2, 97-99) proved, that for any hypergraph F = fF1; F2; : : : ; Fd(q 1)+1g, where q is a primepower, and d denotes the maximal degree of the hypergraph, there exists an F0 F , such that jSF2F0 F j 0 (mod q). We give a direct, alternative proof for this theorem, and we also give an explicit construction of a hypergraph of degree d and size (d2) which does not contain a non-empty sub-hypergraph with a union of size 0 modulo 6.
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ورودعنوان ژورنال:
- Discrete Mathematics & Theoretical Computer Science
دوره 6 شماره
صفحات -
تاریخ انتشار 2003