Enumeration in the lattice of $q$-decreasing words
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909899570544640 |
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| author | Baril, Jean-Luc Hassler, Nathanaël Kirgizov, Sergey |
| author_facet | Baril, Jean-Luc Hassler, Nathanaël Kirgizov, Sergey |
| contents | We prove that the poset of $q$-decreasing words equipped with the componentwise order forms a lattice. We enumerate the join-irreducible elements for arbitrary $q>0$, and for any positive rational number $q$, we determine the number of coverings, intervals and meet-irreducible elements. The latter present the same structure as words over an alphabet of $2\lceil q\rceil+1$ letters avoiding $\lceil q\rceil^2+2\lceil q\rceil-1$ consecutive patterns of length 2. Furthermore, we analyze the asymptotic behavior of several of these quantities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_09480 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Enumeration in the lattice of $q$-decreasing words Baril, Jean-Luc Hassler, Nathanaël Kirgizov, Sergey Combinatorics Discrete Mathematics We prove that the poset of $q$-decreasing words equipped with the componentwise order forms a lattice. We enumerate the join-irreducible elements for arbitrary $q>0$, and for any positive rational number $q$, we determine the number of coverings, intervals and meet-irreducible elements. The latter present the same structure as words over an alphabet of $2\lceil q\rceil+1$ letters avoiding $\lceil q\rceil^2+2\lceil q\rceil-1$ consecutive patterns of length 2. Furthermore, we analyze the asymptotic behavior of several of these quantities. |
| title | Enumeration in the lattice of $q$-decreasing words |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2511.09480 |