# Discrete Mathematics & Theoretical Computer Science

## Volume 6 n° 1 (2003), pp. 41-44

author: | Vince Grolmusz |
---|---|

title: | A Note on Set Systems with no Union of Cardinality 0 Modulo m |

keywords: | hypergraphs, composite modulus, explicit constructions |

abstract: | Alon, Kleitman, Lipton, Meshulam, Rabin and Spencer (Graphs. Combin. 7 (1991),
no. 2, 97-99) proved, that for any hypergraph
,
where ={FF_{1},F_{2},…, F_{d(q-1)+1}}q
is a prime-power, and d denotes the maximal degree
of the hypergraph, there exists an
, such that
F_{0}⊂ F|. We give a direct,
alternative proof for this theorem, and we also show
that an explicit construction exists for a hypergraph
of degree _{F∈F0}F| ≡ 0 (q)d and size
Ω(d which does not
contain a non-empty sub-hypergraph with a union of
size 0 modulo 6, consequently, the theorem does not
generalize for non-prime-power moduli.
^{2})If your browser does not display the abstract correctly (because of the different mathematical symbols) you can look it up in the PostScript or PDF files. |

reference: | Vince Grolmusz (2003),
A Note on Set Systems with no Union of Cardinality 0 Modulo m,
Discrete Mathematics and Theoretical Computer Science 6, pp. 41-44 |

bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |

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