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1. Turning cycle restrictions into mesh patterns via Foata's fundamental transformation.

Author

Claesson, Anders and Ulfarsson, Henning

Subjects
*GENERATING functions, *LOGICAL prediction, *GENERALIZATION
Abstract

An adjacent q -cycle is a natural generalization of an adjacent transposition. We show that the number of adjacent q -cycles in a permutation maps to the sum of occurrences of two mesh patterns under Foata's fundamental transformation. As a corollary we resolve Conjecture 3.14 in the paper "From Hertzprung's problem to pattern-rewriting systems" by the first author. [ABSTRACT FROM AUTHOR]

Published
2024
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