Result: Conjugating cyclic \(n\)-color compositions

Title:
Conjugating cyclic \(n\)-color compositions
Authors:
Hopkins, Brian, Barrón, Jesús Sistos, Wang, Hua
Source:
Utilitas Mathematica. 122:53-64
Publisher Information:
Combinatorial Press, 2025.
Publication Year:
2025
Subject Terms:
Combinatorial aspects of partitions of integers, combinatorial proofs, Exact enumeration problems, generating functions, \(n\)-color compositions, Elementary theory of partitions, integer compositions, Combinatorial identities, bijective combinatorics, cyclic compositions, conjugation
Document Type:
Academic journal Article
File Description:
application/xml
ISSN:
0315-3681
DOI:
10.61091/um122-04
Accession Number:
edsair.doi.dedup.....41ae37d50c5f5cf0577828896dcb9aea
Database:
OpenAIRE

Further Information

MacMahon extensively studied integer compositions, including the notion of conjugation. More recently, Agarwal introduced \(n\)-color compositions and their cyclic versions were considered by Gibson, Gray, and Wang. In this paper, we develop and study a conjugation rule for cyclic \(n\)-color compositions. Also, for fixed \(\ell\), we identify and enumerate the subset of self-conjugate compositions of \(\ell\), as well as establish a bijection between these and the set of cyclic regular compositions of \(\ell\) with only odd parts.