Descent classes of permutations with a given number of fixed points (Q1318370)

A desarrangement is a permutation whose first ascent is even. The first author introduced this class of permutations for the purpose of combinatorially explaining a standard recurrence relation for the number of derangements of \(n\) elements. He gave a nice bijection between derangements and desarrangements and this bijection is extended in the paper under review for obtaining more refined results concerning derangements and desarrangements. In particular, a bijection between descent classes of derangements and descent classes of desarrangements is established. The main result reads: In any (nontrivial) descent class, the number of permutations with exactly \(k\) fixed points decreases as \(k\) increases.