Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A combinatorial proof in terms of Schroder paths and other ighted 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 Schroder paths in a plane.
['Shuhei Kamioka']
I am writing a research paper on a idea A combinatorial derivation with Schroder paths of a determinant representation of Laurent biorthogonal polynomials
[{"from": "human", "value": "I am writing a research paper on a idea A combinatorial derivation with Schroder paths of a determinant representation of Laurent biorthogonal polynomials"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A combinatorial proof in terms of Schroder paths and other ighted 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 Schroder paths in a plane."}]