Pascal's Triangles in Abelian and Hyperbolic Groups

1996/11/27 by Michael Shapiro, Shapiro, Michael · 1 citation
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.math/9611206

DVI file only, 7 pages

arxiv created 1996/11/27 · arxiv updated 2009/11/30

Abstract

Pascal's triangle will give the number of geodesics from the identity to each point of \bf Z² if you write it in each of the quadrants. Given a group G and generating set \cal G we take the \it Pascal's function p_{\cal G}: G → \bf Z_{≥ 0} to be the function which assigns to each g∈ G the number of geodesics from 1 to g. We give a general method for calculating this in hyperbolic groups and discuss the generic case in abelian groups.

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