%D 2024 %V 31 %A B Deb %A AD Sokal %T A Remark on Continued Fractions for Permutations and D-Permutations with a Weight −1 per Cycle %N 2 %X We show that very simple continued fractions can be obtained for the ordinary generating functions enumerating permutations or D-permutations with a large number of independent statistics, when each cycle is given a weight −1. The proof is based on a simple lemma relating the number of cycles modulo 2 to the numbers of fixed points, cycle peaks (or cycle valleys), and crossings. %O This work is licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) License. %I The Electronic Journal of Combinatorics %L discovery10192075 %J Electronic Journal of Combinatorics