Callan permutations and odd order permutations

We call a permutation to be of odd order if writing in cycle form consisting of only odd cycles, and call a permutation to be a Callan permutation if all its left-to-right minima appear at odd positions. This paper aims to provide five elementary proofs that Callan permutations and odd order permuta...

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Bibliographic Details
Published in:Graphs and combinatorics Vol. 41; no. 6; p. 124
Main Authors: Du, Rosena R. X., Lin, Zhicong, Wang, David G. L., Zhao, Tongyuan
Format: Journal Article
Language:English
Published: Tokyo Springer Japan 01.12.2025
Springer Nature B.V
Subjects:
Codes
Combinatorial analysis
Combinatorics
Correspondence
Engineering Design
Mathematics
Mathematics and Statistics
Original Paper
Permutations
Left-to-right minima
Odd cycles
Bijections
Peak values
05A19
05A05
05A15
ISSN:0911-0119, 1435-5914
Online Access:Get full text
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Summary:We call a permutation to be of odd order if writing in cycle form consisting of only odd cycles, and call a permutation to be a Callan permutation if all its left-to-right minima appear at odd positions. This paper aims to provide five elementary proofs that Callan permutations and odd order permutations have the same cardinality: one by generating functions, two by recursions and another two by combinatorial bijections. The last bijection gives rise to a refinement of this equality.
Bibliography:ObjectType-Article-1
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content type line 14
ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-025-02984-9