2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/170752We 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.Ph.D. thesis, University of Colorado, 2008. Advisor: R.M. Green. 21 figuresCombinatoricsQuantum Algebra20F55, 20C08text