Geodesic
A remark on continued fractions for permutations and D-permutations with a weight \(-1\) per cycle
Bishal Deb1 ; Alan D. Sokal2
1University College London
2New York University
The electronic journal of combinatorics, Tome 31 (2024) no. 2
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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.
DOI : 10.37236/12149
Classification : 11A55, 05A19, 05A05, 05A15
Mots-clés : continued fractions, permutations, D-permutations

Bishal Deb  1   ; Alan D. Sokal  2

1 University College London
2 New York University 
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     title = {A remark on continued fractions for permutations and {D-permutations} with a weight \(-1\) per cycle},
     journal = {The electronic journal of combinatorics},
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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, Tome 31 (2024) no. 2. doi: 10.37236/12149

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