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arXiv · 2306.17800

Hopf Algebra on Vincular Permutation Patterns

Joscha Diehl·Emanuele Verri
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Abstract

We introduce a new Hopf algebra that operates on pairs of finite interval partitions and permutations of equal length. This algebra captures vincular patterns, which involve specifying both the permutation patterns and the consecutive occurrence of values. Our motivation stems from linear functionals that encode the number of occurrences of these patterns, and we show that they behave well with respect to the operations of this Hopf algebra.

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Joscha Diehl, Emanuele Verri. 2023-06-30. Hopf Algebra on Vincular Permutation Patterns. https://arxiv.org/abs/2306.17800

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