  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.

Combinatorics