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.

Received: 2020-01-03
Accepted: 2020-08-02
Published online: 2020-12-04
DOI: https://doi.org/10.5802/alco.142
Classification: 05A19,  06A07,  06B10
Keywords: lattice, Catalan number, Cambrian lattice, noncrossing partition, nonkissing complex
@article{ALCO_2020__3_6_1331_0,
     author = {Garver, Alexander and McConville, Thomas},
     title = {Chapoton triangles for nonkissing complexes},
     journal = {Algebraic Combinatorics},
     pages = {1331--1363},
     publisher = {MathOA foundation},
     volume = {3},
     number = {6},
     year = {2020},
     doi = {10.5802/alco.142},
     language = {en},
     url = {alco.centre-mersenne.org/item/ALCO_2020__3_6_1331_0/}
}
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/item/ALCO_2020__3_6_1331_0/

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