Derangements and the $p$-adic incomplete gamma function
Number Theory
2023-03-07 v4 Combinatorics
Abstract
We introduce a -adic analogue of the incomplete gamma function. We also introduce quantities (-values) associated to a function on natural numbers and prove a new characterization of -adic continuity for functions with -integral -values. Combinatorial interpretations for the integral values of the incomplete gamma function and functions with -values zero or one are obtained, which show that these functions count derangements in generalized symmetric groups and permutations with restricted cycle lengths.
Cite
@article{arxiv.2012.04615,
title = {Derangements and the $p$-adic incomplete gamma function},
author = {Andrew O'Desky and David Harry Richman},
journal= {arXiv preprint arXiv:2012.04615},
year = {2023}
}
Comments
26 pages; new material on m-values; revised for clarity