A method for determining the mod-$p^k$ behaviour of recursive sequences
Combinatorics
2025-07-29 v2 Number Theory
Abstract
We present a method for obtaining congruences modulo powers of a prime number~ for combinatorial sequences whose generating function satisfies an algebraic differential equation. This method generalises the one by Kauers and the authors [Electron. J. Combin. 8(2) (2012), Art. P37; arXiv:1107.2015] from to arbitrary primes. Our applications include congruences for numbers of non-crossing graphs and numbers of Kreweras walks modulo powers of~, as well as congruences for Fu\ss-Catalan numbers and blossom tree numbers modulo powers of arbitrary primes.
Cite
@article{arxiv.1508.02580,
title = {A method for determining the mod-$p^k$ behaviour of recursive sequences},
author = {Christian Krattenthaler and Thomas W. Müller},
journal= {arXiv preprint arXiv:1508.02580},
year = {2025}
}
Comments
AmS-LaTeX, 36 pages. Several typos corrected. arXiv admin note: substantial text overlap with arXiv:1107.2015; text overlap with arXiv:1308.2856