Abstract:The partition lattice and noncrossing partition lattice are well studied objects in combinatorics. Given a graph G on vertex set {1, 2, . . . , n}, its bond lattice, L G , is the subposet of the partition lattice formed by restricting to the partitions whose blocks induce connected subgraphs of G. In this article, we introduce a natural noncrossing analogue of the bond lattice, the noncrossing bond poset, N C G , obtained by restricting to the noncrossing partitions of L G .Both the noncrossing partition latti… Show more
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