%0 Journal Article
%@ 1077-8926
%A Deb, B
%A Sokal, AD
%D 2024
%F discovery:10192075
%I The Electronic Journal of Combinatorics
%J Electronic Journal of Combinatorics
%N 2
%T A Remark on Continued Fractions for Permutations and D-Permutations with a Weight −1 per Cycle
%U https://discovery.ucl.ac.uk/id/eprint/10192075/
%V 31
%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.
%Z This work is licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) License.