Séminaire Lotharingien de Combinatoire, 82B.62 (2019), 12 pp.

C. Matthew Farmer and Joshua Hallam

The noncrossing bond poset of a graph

Abstract. Given a graph G with vertices labeled by {1,2,...,n}, the bonds of G are in natural bijection with the set partitions of n. We say a bond is noncrossing if its associated partition is noncrossing. Ordering the noncrossing bonds of G$by inclusion, one gets a noncrossing analogue of the bond lattice of G called the noncrossing bond poset. In this extended abstract we study this poset showing that several properties of the bond lattice have analogues in the noncrossing bond poset.


Received: November 15, 2018. Accepted: February 17, 2019. Final version: April 1, 2019.

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