A method for determining the mod-$2^k$ behaviour of recursive sequences, with applications to subgroup counting

Details A method for determining the mod-$2^k$ behaviour of recursive sequences, with applications to subgroup counting A method for determining the mod-$2^k$ behaviour of recursive sequences, with applications to subgroup counting

2011-07-11

arxiv.org/abs/1107.2015v1

Mathematics

Combinatorics

AmS-LaTeX; 66 pages

Scientific paper

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.

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