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arXiv · 2407.07701

Completing the enumeration of inversion sequences avoiding one or two patterns of length 3

Benjamin Testart
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Abstract

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.

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Benjamin Testart. 2024-07-10. Completing the enumeration of inversion sequences avoiding one or two patterns of length 3. https://doi.org/10.37236/13750

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