Mathematics – Combinatorics
Scientific paper
1999-11-11
Mathematics
Combinatorics
28 Pages, 1998 Preprint
Scientific paper
We 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.
No associations
LandOfFree
Growth in free groups (and other stories) does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Growth in free groups (and other stories), we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Growth in free groups (and other stories) will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-587282