On rank functions for heaps

Authors:
R. M. Green
Affiliations:
Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, UK
Venue:
Journal of Combinatorial Theory Series A
Year:
2003

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Abstract

Motivated by work of Stembridge, we study rank functions for Viennot's heaps of pieces. We produce a simple and sufficient criterion for a heap to be a ranked poset and apply the results to the heaps arising from fully commutative words in Coxeter groups.