Counting Pattern-free Set Partitions II: Noncrossing and Other Hypergraphs

A (multi)hypergraph H with vertices in N contains a permutation p = a1a2 . . . ak of 1, 2, . . . , k if one can reduce H by omitting vertices from the edges so that the resulting hypergraph is isomorphic, via an increasing mapping, to Hp = ({i, k + ai} : i = 1, . . . , k). We formulate six conjectures stating that if H has n vertices and does not contain p then the size of H is O(n) and the number of such Hs is O(cn). The latter part generalizes the Stanley

• Type: Journal
• Year: 2000
• Where: COMBINATORICS
• Authors: Martin Klazar
• Keywords: COMBINATORICS 2000, Hypergraph, Isomorphic, Permutations