AN ANALOGUE OF THE HILTON-MILNER THEOREM FOR WEAK COMPOSITIONS

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 52, Issue 3, 2015, pp.1007-1025
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2015.52.3.1007

Title & Authors

AN ANALOGUE OF THE HILTON-MILNER THEOREM FOR WEAK COMPOSITIONS

Ku, Cheng Yeaw; Wong, Kok Bin;

Ku, Cheng Yeaw; Wong, Kok Bin;

Abstract

Let be the set of non-negative integers, and let P(n, l) denote the set of all weak compositions of n with l parts, i.e., . For any element , denote its ith-coordinate by u(i), i.e., . A family is said to be t-intersecting if for all . A family is said to be trivially t-intersecting if there is a t-set T of and elements such that . We prove that given any positive integers l, t with , there exists a constant depending only on l and t, such that for all , if is non-trivially t-intersecting, then . Moreover, equality holds if and only if there is a t-set T of [l] such that , where and .

Keywords

cross-intersecting family;Hilton-Milner;-Ko-Rado;weak compositions;

Language

English

Cited by

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