Deb, B;
Sokal, AD;
(2024)
A Remark on Continued Fractions for Permutations and D-Permutations with a Weight −1 per Cycle.
Electronic Journal of Combinatorics
, 31
(2)
, Article P2.14. 10.37236/12149.
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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.
| Type: | Article |
|---|---|
| Title: | A Remark on Continued Fractions for Permutations and D-Permutations with a Weight −1 per Cycle |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.37236/12149 |
| Publisher version: | https://doi.org/10.37236/12149 |
| Language: | English |
| Additional information: | This work is licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) License. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10192075 |
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