The 2D Toda hierarchy occupies a central position in the family of integrable hierarchies of
the Toda type. The 1D Toda hierarchy and the Ablowitz–Ladik (aka relativistic Toda) …

Multiparametric families of hypergeometric τ-functions of KP or Toda type serve as
generating functions for weighted Hurwitz numbers, providing weighted enumerations of …

A bstract In this paper we revisit several recent results on monotone and strictly monotone
Hurwitz numbers, providing new proofs. In particular, we use various versions of these …

We study the nn‐point differentials corresponding to Kadomtsev–Petviashvili (KP) tau
functions of hypergeometric type (also known as Orlov–Scherbin partition functions), with an …

We study a-deformation of monotone Hurwitz numbers, obtained by deforming Schur
functions into Jack symmetric functions. We give an evolution equation for this model and …

Abstract The KP and 2D Toda τ τ-functions of hypergeometric type that serve as generating
functions for weighted single and double Hurwitz numbers are related to the topological …

Two methods of constructing 2D Toda τ-functions that are generating functions for certain
geometrical invariants of a combinatorial nature are related. The first involves generation of …

We express the topological expansion of the Jacobi Unitary Ensemble in terms of triple
monotone Hurwitz numbers. This completes the combinatorial interpretation of the …

Double Hurwitz numbers enumerating weighted n-sheeted branched coverings of the
Riemann sphere or, equivalently, weighted paths in the Cayley graph of S n generated by …

A fermionic representation is given for all the quantities entering in the generating function
approach to weighted Hurwitz numbers and topological recursion. This includes: KP and 2 D …