Journal of Algebraic Combinatorics

, Volume 24, Issue 3, pp 263–284

Reduced decompositions and permutation patterns


    • Department of MathematicsMassachusetts Institute of Technology

DOI: 10.1007/s10801-006-0015-6

Cite this article as:
Tenner, B.E. J Algebr Comb (2006) 24: 263. doi:10.1007/s10801-006-0015-6


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.


Reduced decompositionPermutation patternVexillary permutationZonotopal tilingFreely braided permutation

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© Springer Science + Business Media, Inc. 2006