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arXiv · 2210.03621

Sorting permutations with pattern-avoiding machines

Giulio Cerbai
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Abstract

In this work of thesis we introduce and study a new family of sorting devices, which we call pattern-avoiding machines. They consist of two stacks in series, equipped with a greedy procedure. On both stacks we impose a static constraint in terms of pattern containment: reading the content from top to bottom, the first stack is not allowed to contain occurrences of a given pattern $σ$, whereas the second one is not allowed to contain occurrences of $21$. By analyzing the behavior of pattern-avoiding machines, we aim to gain a better understanding of the problem of sorting permutations with two consecutive stacks, which is currently one of the most challenging open problems in combinatorics.

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Giulio Cerbai. 2022-10-07. Sorting permutations with pattern-avoiding machines. https://arxiv.org/abs/2210.03621

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