Chapoton triangles for nonkissing complexes

Garver, Alexander; McConville, Thomas

doi:10.5802/alco.142

Garver, Alexander ¹; McConville, Thomas ²

¹ Department of Mathematics University of Michigan
² Department of Mathematics Kennesaw State University

Algebraic Combinatorics, Volume 3 (2020) no. 6, pp. 1331-1363.

Abstract

We continue the study of the nonkissing complex that was introduced by Petersen, Pylyavskyy, and Speyer and was studied lattice-theoretically by the second author. We introduce a theory of Grid–Catalan combinatorics, given the initial data of a nonkissing complex, and show how this theory parallels the well-known Coxeter–Catalan combinatorics. In particular, we present analogues of Chapoton’s $F$ -triangle, $H$ -triangle, and $M$ -triangle and give both combinatorial and lattice-theoretic interpretations of the objects defining these polynomials. In our Grid–Catalan setting, we prove that our analogue of Chapoton’s $F$ -triangle and $H$ -triangle identity holds, and we conjecture that our analogue of Chapoton’s $F$ -triangle and $M$ -triangle identity also holds.

Received: 2020-01-03
Accepted: 2020-08-02
Published online: 2020-12-04

DOI: 10.5802/alco.142

Classification: 05A19, 06A07, 06B10
Keywords: lattice, Catalan number, Cambrian lattice, noncrossing partition, nonkissing complex

Author's affiliations:

Garver, Alexander ¹; McConville, Thomas ²

¹ Department of Mathematics University of Michigan
² Department of Mathematics Kennesaw State University

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     title = {Chapoton triangles for nonkissing complexes},
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Garver, Alexander; McConville, Thomas. Chapoton triangles for nonkissing complexes. Algebraic Combinatorics, Volume 3 (2020) no. 6, pp. 1331-1363. doi : 10.5802/alco.142. https://alco.centre-mersenne.org/articles/10.5802/alco.142/

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