The $r$-derangement numbers
Number Theory
2018-03-14 v1 Combinatorics
Abstract
The classical derangement numbers count fixed point-free permutations. In this paper we study the enumeration problem of generalized derangements, when some of the elements are restricted to be in distinct cycles in the cycle decomposition. We find exact formula, combinatorial relations for these numbers as well as analytic and asymptotic description. Moreover, we study deeper number theoretical properties, like modularity, -adic valuations, and diophantine problems.
Cite
@article{arxiv.1803.04529,
title = {The $r$-derangement numbers},
author = {Chenying Wang and Piotr Miska and István Mező},
journal= {arXiv preprint arXiv:1803.04529},
year = {2018}
}
Comments
Published in Discrete Mathematics