TY - JOUR AV - public Y1 - 2024/04/19/ SN - 1077-8926 TI - A Remark on Continued Fractions for Permutations and D-Permutations with a Weight ?1 per Cycle ID - discovery10192075 UR - https://doi.org/10.37236/12149 IS - 2 N2 - 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. VL - 31 N1 - This work is licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) License. PB - The Electronic Journal of Combinatorics JF - Electronic Journal of Combinatorics A1 - Deb, B A1 - Sokal, AD ER -