Number of Compositions and Convolved Fibonacci numbers

Details Number of Compositions and Convolved Fibonacci numbers Number of Compositions and Convolved Fibonacci numbers

2010-03-04

arxiv.org/abs/1003.0981v1

Mathematics

Combinatorics

5 pages

Scientific paper

We consider two type of upper Hessenberg matrices which determinants are Fibonacci numbers. Calculating sums of principal minors of the fixed order of the first type leads us to convolved Fibonacci numbers. Some identities for these and for Fibonacci numbers are proved. We also show that numbers of compositions of a natural number with fixed number of ones appear as coefficients of characteristic polynomial of a Hessenberg matrix which determinant is a Fibonacci number. We derive the explicit formula for the number of such compositions, in terms of convolutions of Fibonacci numbers.

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