Counting Pattern-free Set Partitions II: Noncrossing and Other Hypergraphs
Counting Pattern-free Set Partitions II: Noncrossing and Other Hypergraphs
A (multi)hypergraph ${\cal H}$ with vertices in ${\bf N}$ contains a permutation $p=a_1a_2\ldots a_k$ of $1, 2, \ldots, k$ if one can reduce ${\cal H}$ by omitting vertices from the edges so that the resulting hypergraph is isomorphic, via an increasing mapping, to ${\cal H}_p=(\{i, k+a_i\}:\ i=1, \ldots, k)$. We …