Bubble Lattices II: Combinatorics
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866908569613369344 |
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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 |