Geodesic
Sorting inversion sequences
Discrete mathematics & theoretical computer science, Permutation Patterns 2024, Tome 27 (2025) no. 1.

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We consider the avoidance of patterns in inversion sequences that relate sorting via sorting machines including data structures such as pop stacks and stacks. Such machines have been studied under a variety of additional constraints and generalizations, some of which we apply here. We give the classification of several classes of sortable inversion sequences in terms of pattern avoidance. We are able to provide an exact enumeration of some of the sortable classes in question using both classical approaches and a more recent strategy utilizing generating trees. 
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     author = {Mansour, Toufik and Skogman, Howard and Smith, Rebecca},
     title = {Sorting inversion sequences},
     journal = {Discrete mathematics & theoretical computer science},
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     doi = {10.46298/dmtcs.14010},
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     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.14010/}
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Mansour, Toufik; Skogman, Howard; Smith, Rebecca. Sorting inversion sequences. Discrete mathematics & theoretical computer science, Permutation Patterns 2024, Tome 27 (2025) no. 1. doi : 10.46298/dmtcs.14010. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.14010/

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