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{\bf Shuhei Kamioka}
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{\bf A Combinatorial Derivation with Schr\"{o}der Paths of a Determinant Representation of Laurent Biorthogonal Polynomials}
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A combinatorial proof in terms of Schr\"{o}der paths and other
weigh\-ted plane paths is given for a determinant representation of
Laurent biorthogonal polynomials (LBPs) and that of coefficients of
their three-term recurrence equation.  In this process, it is
clarified that Toeplitz determinants of the moments of LBPs and their
minors can be evaluated by enumerating certain kinds of configurations
of Schr\"{o}der paths in a plane.

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