# ALGEBRAIC COMBINATORICS

Chapoton triangles for nonkissing complexes
Algebraic Combinatorics, Volume 3 (2020) no. 6, pp. 1331-1363.

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.

Accepted:
Published online:
DOI: 10.5802/alco.142
Classification: 05A19,  06A07,  06B10
Keywords: lattice, Catalan number, Cambrian lattice, noncrossing partition, nonkissing complex
Garver, Alexander 1; McConville, Thomas 2

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