Joint distributions of statistics over permutations avoiding two patterns of length 3
Finding distributions of permutation statistics over pattern-avoiding classes of permutations attracted much attention in the literature. In particular, Bukata et al. found distributions of ascents and descents on permutations avoiding any two patterns of length 3. In this paper, we generalize these...
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| Vydáno v: | Discrete mathematics and theoretical computer science Ročník 26:1, Permutation...; číslo Special issues |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Discrete Mathematics & Theoretical Computer Science
04.11.2024
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| Témata: | |
| ISSN: | 1365-8050, 1365-8050 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | Finding distributions of permutation statistics over pattern-avoiding classes
of permutations attracted much attention in the literature. In particular,
Bukata et al. found distributions of ascents and descents on permutations
avoiding any two patterns of length 3. In this paper, we generalize these
results in two different ways: we find explicit formulas for the joint
distribution of six statistics (asc, des, lrmax, lrmin, rlmax, rlmin), and also
explicit formulas for the joint distribution of four statistics (asc, des, MNA,
MND) on these permutations in all cases. The latter result also extends the
recent studies by Kitaev and Zhang of the statistics MNA and MND (related to
non-overlapping occurrences of ascents and descents) on stack-sortable
permutations. All multivariate generating functions in our paper are rational,
and we provide combinatorial proofs of five equidistribution results that can
be derived from the generating functions. |
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| ISSN: | 1365-8050 1365-8050 |
| DOI: | 10.46298/dmtcs.12517 |