Elsevier

Discrete Mathematics

Volume 342, Issue 5, May 2019, Pages 1253-1260
Discrete Mathematics

Reduced expressions for the elements in a Bruhat interval

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Abstract

Let (W,S) be a Coxeter system. We study the relation among the reduced expressions of the elements in the interval [y,w]{zWyzw} for any y<w in W. Fix a reduced expression ξ of w. We find some conditions for various expressions ζ to be reduced, where ζ is obtained from ξ by deleting certain factors in S. We investigate the relations among all such ζ which are reduced expressions for either a certain element in [y,w] or some elements with a certain common property.

Keywords

Coxeter groups
Bruhat interval
Reduced expression

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Supported by the NSF of China (11471115), Shanghai Key Laboratory of PMMP, and STCSM (18dz2271000)