eprintid: 10192075 rev_number: 8 eprint_status: archive userid: 699 dir: disk0/10/19/20/75 datestamp: 2024-05-09 15:37:44 lastmod: 2024-05-09 15:37:44 status_changed: 2024-05-09 15:37:44 type: article metadata_visibility: show sword_depositor: 699 creators_name: Deb, B creators_name: Sokal, AD title: A Remark on Continued Fractions for Permutations and D-Permutations with a Weight −1 per Cycle ispublished: pub divisions: UCL divisions: B04 divisions: C06 divisions: F59 note: This work is licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) License. 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. date: 2024-04-19 date_type: published publisher: The Electronic Journal of Combinatorics official_url: https://doi.org/10.37236/12149 oa_status: green full_text_type: pub language: eng primo: open primo_central: open_green verified: verified_manual elements_id: 2273559 doi: 10.37236/12149 lyricists_name: Sokal, Alan lyricists_id: ADSOK62 actors_name: Flynn, Bernadette actors_id: BFFLY94 actors_role: owner full_text_status: public publication: Electronic Journal of Combinatorics volume: 31 number: 2 article_number: P2.14 issn: 1077-8926 citation: 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 <https://doi.org/10.37236/12149>. Green open access document_url: https://discovery.ucl.ac.uk/id/eprint/10192075/1/12149-PDF%20file-49261-1-10-20240409.pdf