Bubble Lattices II: Combinatorics

Fuente: arXiv
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Main Authors: McConville, Thomas, Mühle, Henri
Format: Preprint
Published: 2022
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author McConville, Thomas
Mühle, Henri
author_facet McConville, Thomas
Mühle, Henri
contents We introduce two simplicial complexes, the noncrossing matching complex and the noncrossing bipartite complex. Both complexes are intimately related to the bubble lattice introduced in our earlier article "Bubble Lattices I: Structure" (arXiv:2202.02874). We study these complexes from both an enumerative and a geometric point of view. In particular, we prove that these complexes are shellable and give explicit formulas for certain refined face numbers. Lastly, we conjecture an intriguing connection of these refined face numbers to the so-called M-triangle of the shuffle lattice.
format Preprint
id arxiv_https___arxiv_org_abs_2208_13683
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle Bubble Lattices II: Combinatorics
McConville, Thomas
Mühle, Henri
Combinatorics
05E45, 06A07, 06B99
We introduce two simplicial complexes, the noncrossing matching complex and the noncrossing bipartite complex. Both complexes are intimately related to the bubble lattice introduced in our earlier article "Bubble Lattices I: Structure" (arXiv:2202.02874). We study these complexes from both an enumerative and a geometric point of view. In particular, we prove that these complexes are shellable and give explicit formulas for certain refined face numbers. Lastly, we conjecture an intriguing connection of these refined face numbers to the so-called M-triangle of the shuffle lattice.
title Bubble Lattices II: Combinatorics
topic Combinatorics
05E45, 06A07, 06B99
url https://arxiv.org/abs/2208.13683