Derangements and the $p$adic incomplete gamma function
Abstract
We introduce a $p$adic analogue of the incomplete gamma function. We also introduce quantities ($m$values) associated to a function on natural numbers and prove a new characterization of $p$adic continuity for functions with $p$integral $m$values. Combinatorial interpretations for the integral values of the incomplete gamma function and functions with $m$values zero or one are obtained, which show that these functions count derangements in generalized symmetric groups and permutations with restricted cycle lengths.
 Publication:

arXiv eprints
 Pub Date:
 December 2020
 arXiv:
 arXiv:2012.04615
 Bibcode:
 2020arXiv201204615O
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Combinatorics;
 33B20;
 11S80;
 11B75;
 05A05
 EPrint:
 26 pages