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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Vydáno v:Graphs and combinatorics Ročník 41; číslo 6; s. 124
Hlavní autoři: Du, Rosena R. X., Lin, Zhicong, Wang, David G. L., Zhao, Tongyuan
Médium: Journal Article
Jazyk:angličtina
Vydáno: Tokyo Springer Japan 01.12.2025
Springer Nature B.V
Témata:
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
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-025-02984-9