Geodesic
An Erdős-Ko-Rado theorem for multisets
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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Let $k$ and $m$ be positive integers. A collection of $k$-multisets from $\{1,\dots, m \}$ is intersecting if every pair of multisets from the collection is intersecting. We prove that for $m \geq k+1$, the size of the largest such collection is $\binom{m+k-2}{k-1}$ 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 $m \leq k$ is also given.
DOI : 10.37236/707
Classification : 05D05 
@article{10_37236_707,
     author = {Karen Meagher and Alison Purdy},
     title = {An {Erd\H{o}s-Ko-Rado} theorem for multisets},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/707},
     zbl = {1244.05223},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/707/}
}
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Karen Meagher; Alison Purdy. An Erdős-Ko-Rado theorem for multisets. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/707

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