Bijections on pattern avoiding inversion sequences and related objects
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916195186245632 |
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| author | Huh, JiSun Kim, Sangwook Seo, Seunghyun Shin, Heesung |
| author_facet | Huh, JiSun Kim, Sangwook Seo, Seunghyun Shin, Heesung |
| contents | The number of inversion sequences avoiding two patterns $101$ and $102$ is known to be the same as the number of permutations avoiding three patterns $2341$, $2431$, and $3241$. This sequence also counts the number of Schröder paths without triple descents, restricted bicolored Dyck paths, $(101,021)$-avoiding inversion sequences, and weighted ordered trees. We provide bijections to integrate them together by introducing $F$-paths. Moreover, we define three kinds of statistics for each of the objects and count the number of each object with respect to these statistics. We also discuss direct sums of each object. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04091 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bijections on pattern avoiding inversion sequences and related objects Huh, JiSun Kim, Sangwook Seo, Seunghyun Shin, Heesung Combinatorics Primary 05A19, Secondary 05A05, 05A15 The number of inversion sequences avoiding two patterns $101$ and $102$ is known to be the same as the number of permutations avoiding three patterns $2341$, $2431$, and $3241$. This sequence also counts the number of Schröder paths without triple descents, restricted bicolored Dyck paths, $(101,021)$-avoiding inversion sequences, and weighted ordered trees. We provide bijections to integrate them together by introducing $F$-paths. Moreover, we define three kinds of statistics for each of the objects and count the number of each object with respect to these statistics. We also discuss direct sums of each object. |
| title | Bijections on pattern avoiding inversion sequences and related objects |
| topic | Combinatorics Primary 05A19, Secondary 05A05, 05A15 |
| url | https://arxiv.org/abs/2404.04091 |