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arXiv · 2306.11500

A remark on continued fractions for permutations and D-permutations with a weight $-1$ per cycle

Bishal Deb·Alan D. Sokal
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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.

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Bishal Deb, Alan D. Sokal. 2024-04-18. A remark on continued fractions for permutations and D-permutations with a weight $-1$ per cycle. https://doi.org/10.37236/12149

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