Explicit closed algebraic formulas for Orlov–Scherbin <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>n</mml:mi> </mml:math> -point functions
Boris Bychkov, Petr Dunin‐Barkowski, Maxim Kazarian, Sergey Shadrin
Abstract
We derive a new explicit formula in terms of sums over graphs for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>n</mml:mi> </mml:math> -point correlation functions of general formal weighted double Hurwitz numbers coming from the Kadomtsev–Petviashvili tau functions of hypergeometric type (also known as Orlov–Scherbin partition functions). Notably, we use the change of variables suggested by the associated spectral curve, and our formula turns out to be a polynomial expression in a certain small set of formal functions defined on the spectral curve.
Topics & Concepts
MathematicsHypergeometric functionHypergeometric distributionAlgebraic numberPartition (number theory)CombinatoricsDiscrete mathematicsAlgebra over a fieldPure mathematicsMathematical analysisAlgebraic structures and combinatorial modelsNonlinear Waves and SolitonsAdvanced Combinatorial Mathematics