Growth in free groups (and other stories)

Simple item page
dc.creatorRivin, Igor
dc.date1999-11-11
dc.date1999-12-07
dc.date.accessioned2026-07-07T05:31:33Z
dc.date.available2026-07-07T05:31:33Z
dc.descriptionWe start by studying the distribution of (cyclically reduced) elements of the free groups with respect to their abelianization. We derive an explicit generating function, and a limiting distribution, by means of certain results (of independent interest) on Chebyshev polynomials; we also prove that the reductions $\mod p$ ($p$ -- an arbitrary prime) of these classes are asymptotically equidistributed, and we study the deviation from equidistribution. We extend our techniques to a more general setting and use them to study the statistical properties of long cycles (and paths) on regular (directed and undirected) graphs. We return to the free group to study some growth functions of the number of conjugacy classes as a function of their cyclically reduced length.
dc.description28 Pages, 1998 Preprint
dc.identifierhttps://arxiv.org/abs/math/9911076
dc.identifierhttp://arxiv.org/abs/math/9911076
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/79384
dc.subjectCombinatorics
dc.subjectDynamical Systems
dc.subjectGroup Theory
dc.subjectProbability
dc.subjectRepresentation Theory
dc.subject05C25; 05C20; 05C38; 60J10; 60F05; 42A05; 22E27
dc.titleGrowth in free groups (and other stories)
dc.typetext

Files

Collections

arXiv