A method for determining the mod-$2^k$ behaviour of recursive sequences, with applications to subgroup counting
Combinatorics
2012-06-27 v2 Group Theory
Abstract
We present a method to obtain congruences modulo powers of 2 for sequences given by recurrences of finite depth with polynomial coefficients. We apply this method to Catalan numbers, Fu\ss-Catalan numbers, and to subgroup counting functions associated with Hecke groups and their lifts. This leads to numerous new results, including many extensions of known results to higher powers of 2.
Cite
@article{arxiv.1107.2015,
title = {A method for determining the mod-$2^k$ behaviour of recursive sequences, with applications to subgroup counting},
author = {Manuel Kauers and Christian Krattenthaler and Thomas W. Müller},
journal= {arXiv preprint arXiv:1107.2015},
year = {2012}
}
Comments
AmS-LaTeX; 76 pages; substantial revision: an appendix added which enhances the presented method, many errors and typos corrected; to appear in Electron. J. Combin