Completing the enumeration of inversion sequences avoiding one or two patterns of length 3
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909918126145536 |
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| author | Testart, Benjamin |
| author_facet | Testart, Benjamin |
| contents | We present four constructions of inversion sequences, and use them to compute the enumeration sequences of 24 classes of pattern-avoiding inversion sequences. This completes the enumeration of inversion sequences avoiding one or two patterns of length 3. Some of our constructions are based on generating trees. Others involve pattern-avoiding words, which we also count using generating trees. To solve some of these cases, we introduce a generalization of inversion sequences, which we call shifted inversion sequences. Lastly, we briefly discuss the asymptotics of pattern-avoiding inversion sequences, focusing on their exponential or super-exponential behavior. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_07701 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Completing the enumeration of inversion sequences avoiding one or two patterns of length 3 Testart, Benjamin Combinatorics We present four constructions of inversion sequences, and use them to compute the enumeration sequences of 24 classes of pattern-avoiding inversion sequences. This completes the enumeration of inversion sequences avoiding one or two patterns of length 3. Some of our constructions are based on generating trees. Others involve pattern-avoiding words, which we also count using generating trees. To solve some of these cases, we introduce a generalization of inversion sequences, which we call shifted inversion sequences. Lastly, we briefly discuss the asymptotics of pattern-avoiding inversion sequences, focusing on their exponential or super-exponential behavior. |
| title | Completing the enumeration of inversion sequences avoiding one or two patterns of length 3 |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2407.07701 |