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arXiv · 2602.12130

On minimal pattern-containing inversion sequences

Benjamin Testart
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Abstract

We introduce the notion of minimal inversion sequences for a pattern $\rho$, which form the smallest set of inversion sequences whose avoidance is equivalent to the avoidance of $\rho$ for inversion sequences. We give a characterization of $\rho$-minimal inversion sequences based on the occurrences of the pattern $\rho$ they contain, and use it to find upper and lower bounds on the lengths of $\rho$-minimal inversion sequences. We provide some enumerative results on the exact number of minimal inversion sequences for some patterns, through a bijection with increasing trees, and some exhaustive generation. Lastly, we enumerate inversion sequences which are equal to their reduction, and find an interesting connection with poly-Bernoulli numbers.

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Benjamin Testart. 2026-02-12. On minimal pattern-containing inversion sequences. https://arxiv.org/abs/2602.12130

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