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. |

ps.gz-source: | dm060103.ps.gz (17 K) |

ps-source: | dm060103.ps (41 K) |

pdf-source: | dm060103.pdf (64 K) |

The first *source* gives you the `gzipped' PostScript, the second the plain
PostScript and the third the format for the Adobe accrobat
reader. Depending on the installation of your web browser, at least
one of these should (after some amount of time) pop up a window for
you that shows the full article. If this is not the case, you should
contact your system administrator to install your browser correctly.

Due to limitations of your local software, the two formats may show up differently on your screen. If eg you use xpdf to visualize pdf, some of the graphics in the file may not come across. On the other hand, pdf has a capacity of giving links to sections, bibliography and external references that will not appear with PostScript.

Automatically produced on mer avr 16 11:36:26 CEST 2003 by gustedt