Planar superconformal Yang-Mills determinant observables are shown to equal generalized Dyck path partition functions through a universal iterated integral expansion.
Determinant Formulas for the Toda and Discrete Toda Equations
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Determinant formulas for the general solutions of the Toda and discrete Toda equations are presented. Application to the $\tau$ functions for the Painlev\'e equations is also discussed.
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Lattice path combinatorics in superconformal Yang-Mills theories
Planar superconformal Yang-Mills determinant observables are shown to equal generalized Dyck path partition functions through a universal iterated integral expansion.