Canon permutations and generalized descents of standard Young tableaux
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914724701011968 |
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| author | Elizalde, Sergi |
| author_facet | Elizalde, Sergi |
| contents | Canon permutations are permutations of the multiset having $k$ copies of each integer between $1$ and $n$, with the property that the subsequences obtained by taking the $j$th copy of each entry, for each fixed $j$, are all the same. For $k=2$, canon permutations are sometimes called nonnesting permutations, and it is known that the polynomial that enumerates them by the number of descents factors as a product of an Eulerian polynomial and a Narayana polynomial. We extend this result to arbitrary $k$, and we relate the problem to the enumeration of standard Young tableaux of rectangular shape with respect to generalized descent statistics. Our proof is bijective, and it also settles a conjecture of Sulanke about the distribution of certain lattice path statistics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_14914 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Canon permutations and generalized descents of standard Young tableaux Elizalde, Sergi Combinatorics 05A15, 05A19, 05A05 Canon permutations are permutations of the multiset having $k$ copies of each integer between $1$ and $n$, with the property that the subsequences obtained by taking the $j$th copy of each entry, for each fixed $j$, are all the same. For $k=2$, canon permutations are sometimes called nonnesting permutations, and it is known that the polynomial that enumerates them by the number of descents factors as a product of an Eulerian polynomial and a Narayana polynomial. We extend this result to arbitrary $k$, and we relate the problem to the enumeration of standard Young tableaux of rectangular shape with respect to generalized descent statistics. Our proof is bijective, and it also settles a conjecture of Sulanke about the distribution of certain lattice path statistics. |
| title | Canon permutations and generalized descents of standard Young tableaux |
| topic | Combinatorics 05A15, 05A19, 05A05 |
| url | https://arxiv.org/abs/2403.14914 |