Séminaire Lotharingien de Combinatoire, 82B.12 (2019), 12 pp.
Yann Palu, Vincent Pilaud, and Pierre-Guy Plamondon
Non-kissing versus non-crossing
Abstract.
Starting from a locally gentle bound quiver, we define on the one hand a simplicial complex, called the non-kissing complex. On the other hand, we construct a punctured, marked, oriented surface with boundary, endowed with a pair of dual dissections. From those geometric data, we define two simplicial complexes: the accordion complex, and the slalom complex, generalizing work of A. Garver and T. McConville in the case of a disk. We show that all three complexes are isomorphic.
Received: November 15, 2018.
Accepted: February 17, 2019.
Final version: April 1, 2019.
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