An Erdős-Ko-Rado theorem for multisets [article]

Karen Meagher, Alison Purdy
<span title="2011-11-18">2011</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Let k and m be positive integers. A collection of k-multisets from {1,..., m } is intersecting if every pair of multisets from the collection is intersecting. We prove that for m ≥ k+1, the size of the largest such collection is m+k-2k-1 and that when m > k+1, only a collection of all the k-multisets containing a fixed element will attain this bound. The size and structure of the largest intersecting collection of k-multisets for m ≤ k is also given.
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="">arXiv:1111.4493v1</a> <a target="_blank" rel="external noopener" href="">fatcat:d6pqiyz6vvbyncguarlqyx7oce</a> </span>
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