Abstract:We give a combinatorial interpretation of vector continued fractions obtained by applying the Jacobi-Perron algorithm to a vector of p ≥ 1 resolvent functions of a banded Hessenberg operator of order p + 1. The interpretation consists in the identification of the coefficients in the Laurent series expansion of the resolvent functions as weight polynomials associated with certain collections of lattice paths. In the scalar case p = 1 this reduces to the relation established by P. Flajolet between Jacobi continu… Show more
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