@article{discovery10192075, note = {This work is licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) License.}, number = {2}, journal = {Electronic Journal of Combinatorics}, year = {2024}, title = {A Remark on Continued Fractions for Permutations and D-Permutations with a Weight ?1 per Cycle}, volume = {31}, month = {April}, publisher = {The Electronic Journal of Combinatorics}, author = {Deb, B and Sokal, AD}, url = {https://doi.org/10.37236/12149}, abstract = {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.}, issn = {1077-8926} }