2006/06/12 by Miklós Bóna, Bona, Miklos
Computer Science · Mathematics · #05A05 05A15 05A16 #Advanced Combinatorial Mathematics #Complex Variables (math.CV) #Computational Geometry and Mesh Generation #Data Management and Algorithms #FOS: Mathematics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.math/0606277
openalex publication_date 2006/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove an interesting fact describing the location of the roots of the generating polynomials of the numbers of derangements of length n, counted by their number of cycles. We then use this result to prove that if k is the number of cycles of a randomly selected derangement of length n, then the probability that k is congruent to a given r modulo a given q converges to 1/q. Finally, we generalize our results to a-derangements, which are permutations in which each cycle is longer than a.