Conjoined permutation patterns

Abstract: Some time ago, Bandt introduced the concept of "permutation entropy" which proved very effective in the analysis of time series. This index is based on certain permutation patterns. Permutation patterns play indeed a very central role in many areas of discrete mathematics. More recently, in algebraic combinatorics, Vargas introduced the superinfiltration Hopf algebra whose operations behave well with respect to occurrences of permutation patterns. Inspired by both these works, we introduce a new Hopf algebra which also includes the patterns used by Bandt. Its algebraic operations behave well with respect to occurrences of permutation patterns where is also specified whether values are consecutive or arbitrarily far apart. To encode whether two values are consecutive, we use interval partitions of finite subsets of positive integers and also introduce a new Hopf algebra on interval partitions. This is joint work with Joscha Diehl.

Computer sciencecommutative algebracombinatoricsrings and algebras

Audience: researchers in the topic

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Algebraic and Combinatorial Perspectives in the Mathematical Sciences

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