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Pascal's triangles in Abelian and hyperbolic groups

Part of: Combinatorics

Published online by Cambridge University Press:  09 April 2009

Michael Shapiro
Michael Shapiro
Affiliation:
Department of Mathematics and Statistics University of MelbourneParkville, VIC 3052Australia e-mail: shapiro@ms.unimelb.edu.au
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Abstract

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Given a group G and a finite generating set G, we take pG: G → Z to be the function which counts the number of geodesics for each group element g. This generalizes Pascal's triangle. We compute pG for word hyperbolic and describe generic behaviour in abelian groups.

MSC classification

Secondary: 05A15: Exact enumeration problems, generating functions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 63 , Issue 2 , October 1997 , pp. 281 - 288
Copyright
Copyright © Australian Mathematical Society 1997

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