A Multiple Integral Explicit Evaluation Inspired by the Multi-WZ Method

Enumerative problems inspired by Mayer's theory of cluster integrals

The basic functional equations for connected and 2-connnected graphs can be traced back to the statistical physicists Mayer and Husimi. They play an essential role in establishing rigorously the virial expansion for imperfect gases. We survey this approach and inspired by these equations, we investigate the problem of enumerating some classes of connected graphs all of whose blocks are contained in a given class B. Included are the species of Husimi graphs (B = "complete graphs"), cacti (B = "unoriented cycles"), and oriented cacti (B = "oriented cycles"). For each of these, we consider the qu…

Integral Representation and Computation a Multiple Sum in the Theory of Cubature Formulas

In this article we furnish a new simple proof of a hard identity from the theory of cubature formulas via the method of coefficients.

Discrete path integral approach to the trace formula for regular graphs

We give a new proof of the trace formula for regular graphs. Our approach is inspired by path integral approach in quantum mechanics, and calculations are mostly combinatorial.

Inversion of integral series enumerating planar trees

We consider an integral series f(X,t) which depends on the choice of a set X of labelled planar rooted trees. We prove that its inverse for composition is of the form f(Z,t) for another set Z of trees, deduced from X. The proof is self-contained, though inspired by the Koszul duality theory of quadratic operads.

多重排列的导子的积分表达式

Integral expressions for derivations of multiarrangements

本文受量子Calogero-Moser系统拟不变量积分表达式的启发，为若干自由多重排列构造了特定基的积分表达式，并推广到二维三直线及复反射群相关情形，还对类型B_2扩展Catalan排列的对数向量场模提出猜想性基。