Pattern Avoidance in Weak Ascent Sequences
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866912011537874944 |
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| author | Bényi, Beáta Mansour, Toufik Ramírez, José L. |
| author_facet | Bényi, Beáta Mansour, Toufik Ramírez, José L. |
| contents | In this paper, we study pattern avoidance in weak ascent sequences, giving some results for patterns of length 3. This is an analogous study to one given by Duncan and Steingrímsson (2011) for ascent sequences. More precisely, we provide systematically the generating functions for the number of weak ascent sequences avoiding the patterns $001, 011, 012, 021$, and $102$. Additionally, we establish bijective connections between pattern-avoiding weak ascent sequences and other combinatorial objects, such as compositions, upper triangular 01-matrices, and plane trees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_06518 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Pattern Avoidance in Weak Ascent Sequences Bényi, Beáta Mansour, Toufik Ramírez, José L. Combinatorics 05A05, 05A15, 05A19 In this paper, we study pattern avoidance in weak ascent sequences, giving some results for patterns of length 3. This is an analogous study to one given by Duncan and Steingrímsson (2011) for ascent sequences. More precisely, we provide systematically the generating functions for the number of weak ascent sequences avoiding the patterns $001, 011, 012, 021$, and $102$. Additionally, we establish bijective connections between pattern-avoiding weak ascent sequences and other combinatorial objects, such as compositions, upper triangular 01-matrices, and plane trees. |
| title | Pattern Avoidance in Weak Ascent Sequences |
| topic | Combinatorics 05A05, 05A15, 05A19 |
| url | https://arxiv.org/abs/2309.06518 |