Séminaire Lotharingien de Combinatoire, 86B.63 (2022), 12 pp.
Thomas McConville and Henri Mühle
Shuffle Lattices and Bubble Lattices
Abstract.
C. Greene introduced the shuffle lattice as an idealized model for DNA mutation and discovered remarkable combinatorial and enumerative properties of these structures. In this article we attempt an explanation of these properties from a lattice-theoretic point of view. To that end, we introduce and study an order extension of the shuffle lattice, the {bubble lattice. Intriguingly, most of the combinatorics of the bubble lattice can be encoded by means of two simplicial complexes, the {noncrossing matching complex and the {noncrossing bipartite complex. We present an intriguing relationship between the f-vectors of these complexes and relate it to the rank-generating function of the shuffle lattice.
Received: November 25, 2021.
Accepted: March 4, 2022.
Final version: April 1, 2022.
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