Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5776923 | Discrete Mathematics | 2017 | 12 Pages |
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, p-adic valuations, and diophantine problems.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Chenying Wang, Piotr Miska, István MezÅ,