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Determinants and Compositions of Natural Numbers

Name: Determinants and Compositions of Natural Numbers
Creator: Janjic, Milan
Keywords: FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO)

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2010Embargo end date: 01 Jan 2010Publisher:arXiv

Authors: Janjic, Milan;

doi: 10.48550/arxiv.1007.0526

arXiv: http://arxiv.org/abs/1007.0526

Determinants and Compositions of Natural Numbers

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Abstract

We consider a particular type of matrices which belong at the same time to the class of Hessenberg and Toeplitz matrices, and whose determinants are equal to the number of a type of compositions of natural numbers. We prove a formula in which the number of weak compositions with a fixed number of zeroes is expressed in terms of the number of compositions without zeroes. Then we find a relationship between weak compositions and coefficients of characteristic polynomials of appropriate matrices. Finally, we prove three explicit formulas for weak compositions of a special kind.

Keywords

FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO)

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