Reduced Decompositions and Permutation Patterns

Bridget Eileen Tenner

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Reduced Decompositions and Permutation Patterns

Bridget Eileen Tenner

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Abstract

Billey, Jockusch, and Stanley characterized 321-avoiding permutations by a property of their reduced decompositions. This paper generalizes that result with a detailed study of permutations via their reduced decompositions and the notion of pattern containment. These techniques are used to prove a new characterization of vexillary permutations in terms of their principal dual order ideals in a particular poset. Additionally, the combined frameworks yield several new results about the commutation classes of a permutation. In particular, these describe structural aspects of the corresponding graph of the classes and the zonotopal tilings of a polygon defined by Elnitsky that is associated with the permutation.

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Bridget Eileen Tenner. 2006-02-17. Reduced Decompositions and Permutation Patterns. https://arxiv.org/abs/math/0506242

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