Determinants and Compositions of Natural Numbers
Combinatorics
2010-07-06 v1
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
Cite
@article{arxiv.1007.0526,
title = {Determinants and Compositions of Natural Numbers},
author = {Milan Janjic},
journal= {arXiv preprint arXiv:1007.0526},
year = {2010}
}