Related papers: Generating weighted Hurwitz numbers
We discuss a method for computing the generating function for the multiplicity distribution in field theories with strong time dependent external sources. At leading order, the computation of the generating function reduces to finding a…
The connection between the generating functions of various sets of tableaux and the appropriate families of quasisymmetric functions is a significant tool to give a direct analytical proof of some advanced bijective results and provide new…
In this letter we continue the development of $W$-representations. We propose several generalizations of the known models, such as the hypergeometric Hurwitz $\tau$-functions. We construct $W$-representations for multi-character expansions,…
We consider the general form of "Correlated Worldline" (CWL) theories of quantum gravity. We show that one can have 2 different kinds of CWL theory, in which the generating functional is written as either a sum or a product over multiple…
We prove that the logarithm of an arbitrary tau-function of the KdV hierarchy can be approximated, in the topology of graded formal series by the logarithmic expansions of hyperelliptic theta-functions of finite genus, up to at most…
We define a new Hurwitz problem which is essentially a small core of the simple Hurwitz problem. The corresponding Hurwitz numbers have simpler formulae, satisfy effective recursion relations and determine the simple Hurwitz numbers. We…
In general, Hurwitz numbers count branched covers of the Riemann sphere with prescribed ramification data, or equivalently, factorisations in the symmetric group with prescribed cycle structure data. In this paper, we initiate the study of…
We establish the meromorphic continuation of certain multiple zeta functions of generalized Hurwitz type. From this meromorphic continuation, we obtain explicit formulas for their (derivative) values at nonpositive integers along a given…
We investigate some weighted integer partitions whose generating functions are double-series. We will establish closed formulas for these $q$-double series and deduce that their coefficients are non-negative. This leads to inequalities…
In this paper we establish relations between three enumerative geometry tau-functions, namely the Kontsevich-Witten, Hurwitz and Hodge tau-functions. The relations allow us to describe the tau-functions in terms of matrix integrals,…
We consider a new type of Hurwitz number, the number of ordered transitive factorizations of an arbitrary permutation into d-cycles. In this paper, we focus on the special case d = 3. The minimal number of transitive factorizations of any…
We define a parametric variant of generalized Euler sums and construct contour integration to give some explicit evaluations of these parametric Euler sums. In particular, we establish several explicit formulas of (Hurwitz) zeta functions,…
The generating function method that we had developing has various applications in physics and not only interress undergraduate students but also physicists. We solve simply difficult problems or unsolved commonly used in quantum, nuclear…
Multivariate hypergeometric functions associated with toric varieties were introduced by Gel'fand, Kapranov and Zelevinsky. Singularities of such functions are discriminants, that is, divisors projectively dual to torus orbit closures. We…
This announcement paper summarises recent development concerning the generalized cosecant numbers $c_{\rho,k}$, which represent the coefficients of the power series expansion for the important fundamental function $z^{\rho}/\sin^{\rho} z$.…
The hyperharmonic numbers h_{n}^{(r)} are defined by means of the classical harmonic numbers. We show that the Euler-type sums with hyperharmonic numbers: {\sigma}(r,m)=\sum_{n=1}^{\infty}((h_{n}^{(r)})/(n^{m})) can be expressed in terms of…
The classical Hurwitz numbers which count coverings of a complex curve have an analog when the curve is endowed with a theta characteristic. These "spin Hurwitz numbers", recently studied by Eskin, Okounkov and Pandharipande, are…
We introduce a new matrix model representation for the generating function of simple Hurwitz numbers. We calculate the spectral curve of the model and the associated symplectic invariants developed in [Eynard-Orantin]. As an application, we…
The existing formalism used to compute the operator overlaps necessary to carry out generator coordinate method calculations using a set of Hartree- Fock- Bogoliubov wave functions, is generalized to the case where each of the HFB states…
The semisimple Frobenius manifolds related to the Hurwitz spaces $H_{g,N}(k_1, ..., k_l)$ are considered. We show that the corresponding isomonodromic tau-function $\tau_I$ coincides with $(-1/2)$-power of the Bergmann tau-function which…