We study noncommutative continuant polynomials via a new leapfrog construc- tion. This needs the introduction of new indeterminates and leads to generalizations of Fibonacci polynomials, Lucas polynomials and other families of polynomials. We relate these polynomials to various topics such as quiver algebras and tilings. Finally, we use permanents to give a broad perspective on the subject.
Leapfrog constructions: From continuant polynomials to permanents of matrices
FACCHINI, ALBERTO;
2015
Abstract
We study noncommutative continuant polynomials via a new leapfrog construc- tion. This needs the introduction of new indeterminates and leads to generalizations of Fibonacci polynomials, Lucas polynomials and other families of polynomials. We relate these polynomials to various topics such as quiver algebras and tilings. Finally, we use permanents to give a broad perspective on the subject.
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