Conjugating cyclic n-color compositions

Brian Hopkins; Jesús Sistos Barrón; Hua Wang

doi:10.61091/um122-04

Conjugating cyclic n-color compositions

Brian Hopkins, Jesús Sistos Barrón, Hua Wang

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

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 xed ℓ, we identify and enumerate the subset of self-conjugate compositions of ℓ, as well as establish a bijection between these and the set of cyclic regular compositions of ℓ with only odd parts.

Original language	English
Pages (from-to)	53-64
Number of pages	12
Journal	Utilitas Mathematica
Volume	122
DOIs	https://doi.org/10.61091/um122-04
State	Published - 2025

Scopus Subject Areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

Keywords

combinatorial proofs
conjugation
cyclic compositions
integer compositions
n-color compositions

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10.61091/um122-04

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AB - 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 xed ℓ, we identify and enumerate the subset of self-conjugate compositions of ℓ, as well as establish a bijection between these and the set of cyclic regular compositions of ℓ with only odd parts.

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KW - n-color compositions

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Conjugating cyclic n-color compositions

Abstract

Scopus Subject Areas

Keywords

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