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  -