Reduced decompositions and permutation patterns
- Bridget Eileen Tenner
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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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- Reduced decompositions and permutation patterns
Journal of Algebraic Combinatorics
Volume 24, Issue 3 , pp 263-284
- Cover Date
- Print ISSN
- Online ISSN
- Springer US
- Additional Links
- Reduced decomposition
- Permutation pattern
- Vexillary permutation
- Zonotopal tiling
- Freely braided permutation
- Author Affiliations
- 1. Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, 02139, USA