Leapfrog Constructions: From Continuant Polynomials to Permanents of Matrices

  • Alberto Facchini
  • André Leroy
Keywords: Sequences of polynomials, Fibonacci polynomials, Quiver, Tilings


We study noncommutative continuant polynomials via a new leapfrog construction. 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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