On 102-avoiding inversion sequences
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910983458390016 |
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| author | Huh, JiSun Kim, Sangwook Seo, Seunghyun Shin, Heesung |
| author_facet | Huh, JiSun Kim, Sangwook Seo, Seunghyun Shin, Heesung |
| contents | In this article, we provide a bijection between the set of inversion sequences avoiding the pattern 102 and the set of 2-Schröder paths having neither peaks nor valleys and ending with a diagonal step. To achieve this, we introduce two intermediate objects, called UVD paths and labeled $F$-paths, and establish bijections among all four families. For each of these combinatorial objects, we define a natural statistic and enumerate the corresponding structures with respect to this statistic. In addition, we study inversion sequences avoiding 102 and another pattern of length 3, providing refined enumerations according to the same statistic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_02985 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On 102-avoiding inversion sequences Huh, JiSun Kim, Sangwook Seo, Seunghyun Shin, Heesung Combinatorics Primary 05A19, Secondary 05A05, 05A15 In this article, we provide a bijection between the set of inversion sequences avoiding the pattern 102 and the set of 2-Schröder paths having neither peaks nor valleys and ending with a diagonal step. To achieve this, we introduce two intermediate objects, called UVD paths and labeled $F$-paths, and establish bijections among all four families. For each of these combinatorial objects, we define a natural statistic and enumerate the corresponding structures with respect to this statistic. In addition, we study inversion sequences avoiding 102 and another pattern of length 3, providing refined enumerations according to the same statistic. |
| title | On 102-avoiding inversion sequences |
| topic | Combinatorics Primary 05A19, Secondary 05A05, 05A15 |
| url | https://arxiv.org/abs/2506.02985 |