相关论文: Some relations for one-part double Hurwitz numbers

The generating function of double Hurwitz numbers is known to become a tau function of the Toda hierarchy. The associated Lax and Orlov-Schulman operators turn out to satisfy a set of generalized string equations. These generalized string…

The notes contain a streamlined account on stability of univariate polynomials and related problems

The purpose of these notes is to give a short survey of an interesting connection between partition functions of supersymmetric gauge theories and hypergeometric functions and to present the recent progress in this direction.

This short note addresses Hodge integrals over the hyperelliptic locus. Recently Afandi computed, via localisation techniques, such one-descendant integrals and showed that they are Stirling numbers. We give another proof of the same…

In this note we derive asymptotic formulas for power mean of the Hurwitz zeta function over large intervals.

We classify integrable scalar polynomial partial differential equations of second order generalizing the short pulse equation.

In this paper we present some observations about the well-known Goldbach conjecture. In particular we list and interpret some numerical results which allow us to formulate a relation between prime numbers and even integers. We can also…

In this paper, we present some Hurwitz-Hodge integral identities which are derived from the Laplace transform of the cut-and-join equation for the orbifold Hurwitz numbers. As an application, we prove a conjecture on Hurwitz-Hodge integral…

We prove some combinatorial results related to a formula on Hodge integrals conjectured by Mari\~no and Vafa. These results play important roles in the proof and applications of this formula by the author jointly with Chiu-Chu Melissa Liu…

This note presents several conditions to characterize real matrix similarity between a Hurwitz matrix (and then more generally, a real square matrix) and a diagonal dominant matrix.

We are building a theory of simple Hurwitz numbers for the reflection groups B and D parallel to the classical theory for the symmetric group. We also study analogs of the cut-and-join operators. An algebraic description of Hurwitz numbers…

In this note, we prove the existence of infinitely many zeros of certain generalized Hurwitz zeta functions in the domain of absolute convergence. This is a generalization of a classical problem of Davenport, Heilbronn and Cassels about the…

We show that the Hurwitz problem for sums of squares can depend on the base field. More precisely, we construct an explicit formula of type $[12,12,18]$ over every field of characteristic different from $2$ in which $-1$ is a square,…

We give a general method to reduce Hurewicz-type selection hypotheses into standard ones. The method covers the known results of this kind and gives some new ones. Building on that, we show how to derive Ramsey theoretic characterizations…

Hurwitz numbers count genus $g$, degree $d$ covers of the complex projective line with fixed branched locus and fixed ramification data. An equivalent description is given by factorisations in the symmetric group. Simple double Hurwitz…

We define the double Gromov-Witten invariants of Hirzebruch surfaces in analogy with double Hurwitz numbers, and we prove that they satisfy a piecewise polynomiality property analogous to their 1-dimensional counterpart. Furthermore we show…

In this note, we derive a Leibniz rule for difference quotient.

In this note we will present a supplement to Scholz's reciprocity law and discuss applications to the structure of 2-class groups of quadratic number fields.

This note is a compilation of related research on modular relations for multiple zeta values. Roughly speaking, modular relations are (homogeneous) linear relations of multiple zeta values of fixed weight whose coefficients are `originated'…

We show how to compute the low Hochschild cohomology groups of a partial relation extension algebra.