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Pascal's triangles in Abelian and hyperbolic groups

Published online by Cambridge University Press:  09 April 2009

Michael Shapiro
Affiliation:
Department of Mathematics and Statistics University of MelbourneParkville, VIC 3052Australia e-mail: [email protected]
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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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1997

References

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