On Number of Compositions of Natural Numbers
Milan Janjic (Department of Mathematics, Informatics, University of, Banja Luka, Republic of Srpska)
TL;DR
This paper explores the combinatorial interpretation of Chebyshev polynomial coefficients, linking them to compositions of natural numbers, and investigates relationships between specific composition counts and matrix minors.
Contribution
It introduces a novel combinatorial interpretation of Chebyshev coefficients and connects composition counts with matrix principal minors.
Findings
Established a combinatorial interpretation of Chebyshev coefficients
Derived relationships between different types of compositions of natural numbers
Linked compositions to principal minors of Hessenberg matrices
Abstract
We first give a combinatorial interpretation of coefficients of Chebyshev polynomials, which allows us to connect them with compositions of natural numbers. Then we describe a relationship between the number of compositions of a natural number in which a certain number of parts are p-1, and other parts are not less than p with compositions in which all parts are not less than p. Then we find a relationship between principal minors of a type of Hessenberg matrices and compositions of natural numbers.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Mathematical Identities · Analytic Number Theory Research