A sum rule for derangements
arXiv:2509.14672
Abstract
We propose a sum rule for derangements. Three different proofs are provided. The first one involves integral representations and the second one relies on the Hermite identity for the integer part of the product of an integer by a real number. The third one, which, unlike the previous ones, is not based on induction, proceeds directly from a recurrence relation for the number of derangements.
arXiv commentsubmitted to the journal "Integers"