Geodesic
Completing the enumeration of inversion sequences avoiding one or two patterns of length 3
Benjamin Testart1
1Université de Lorraine
The electronic journal of combinatorics, Tome 32 (2025) no. 4

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Zbl DOI arXiv
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.
DOI : 10.37236/13750
Classification : 05A05, 05A15
Mots-clés : pattern-avoiding inversion sequences, pattern-avoiding words

Benjamin Testart  1

1 Université de Lorraine 
Benjamin Testart. Completing the enumeration of inversion sequences avoiding one or two patterns of length 3. The electronic journal of combinatorics, Tome 32 (2025) no. 4. doi: 10.37236/13750
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     title = {Completing the enumeration of inversion sequences avoiding one or two patterns of length 3},
     journal = {The electronic journal of combinatorics},
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     volume = {32},
     number = {4},
     doi = {10.37236/13750},
     zbl = {arXiv:2407.07701},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/13750/}
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