A discrete isodiametric result: the Erd\H{o}s-Ko-Rado theorem for multisets

Zoltán Füredi; Dániel Gerbner; Máté Vizer

A discrete isodiametric result: the Erd\H{o}s-Ko-Rado theorem for multisets

Combinatorics 2014-03-11 v2

Authors: Zoltán Füredi , Dániel Gerbner , Máté Vizer

Abstract

There are many generalizations of the Erd\H{o}s-Ko-Rado theorem. We give new results (and problems) concerning families of $t$ -intersecting $k$ -element multisets of an $n$ -set and point out connections to coding theory and classical geometry. We establish the conjecture that for $n \geq t(k-t)+2$ such a family can have at most ${n+k-t-1\choose k-t}$ members.

Keywords

Erdős-Ko-Rado theorem multisets t-intersecting families coding theory classical geometry extremal set theory

Cite

@article{arxiv.1212.1071,
  title  = {A discrete isodiametric result: the Erd\H{o}s-Ko-Rado theorem for multisets},
  author = {Zoltán Füredi and Dániel Gerbner and Máté Vizer},
  journal= {arXiv preprint arXiv:1212.1071},
  year   = {2014}
}

A discrete isodiametric result: the Erd\H{o}s-Ko-Rado theorem for multisets

Abstract

Keywords

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