2008/10/05 by Brent G. Pohlmann, Pohlmann, Brent G.
Mathematics · #20C08 #20F55 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Quantum Algebra (math.QA) #math.CO #math.QA #msc:20C08 #msc:20F55
paper · pdf · doi:10.48550/arxiv.0810.0842
Ph.D. thesis, University of Colorado, 2008. Advisor: R.M. Green. 21 figures
arxiv created 2008/10/05 · openalex publication_date 2008/10/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the notions of boundary vertex, linear equivalence and effective boundary vertex in the context of Viennot's heaps of pieces. We prove that in the heap of a fully commutative element in a star reducible Coxeter group, every boundary vertex is linearly equivalent to an effective boundary vertex. Using this result, we establish Property W (in the sense of math.QA/0509363) for star reducible Coxeter groups; this corrects a mistake in the latter paper.