A Remark on Continued Fractions for Permutations and D-Permutations with a Weight -1 per Cycle - Archive ouverte HAL
Article Dans Une Revue The Electronic Journal of Combinatorics Année : 2024

A Remark on Continued Fractions for Permutations and D-Permutations with a Weight -1 per Cycle

Résumé

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.
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Dates et versions

hal-04717244 , version 1 (01-10-2024)

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Bishal Deb, Alan D Sokal. A Remark on Continued Fractions for Permutations and D-Permutations with a Weight -1 per Cycle. The Electronic Journal of Combinatorics, 2024, 31 (2), pp.P2.14. ⟨10.37236/12149⟩. ⟨hal-04717244⟩
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