相关论文: Diagonal Sums of Boxed Plane Partitions

We characterize the measures on R which have both their support and spectrum uniformly discrete. A similar result is obtained in R^n for positive measures.

We prove a relative isoperimetric inequalities for Lagrangian half disks in $\mathbb{C}^2$ with respect to a Lagrangian plane, or a complex plane, or a union of any two of Lagrangian or complex planes that intersect transversally at the…

Given an integer partition of $n$ into distinct parts, the sum of the reciprocal parts is an example of an egyptian fraction. We study this statistic under the uniform measure on distinct parts partitions of $n$ and prove that, as $n \to…

We study the plane automorphisms given by polynomials with certain degree decompositions.

In this paper we present multivariate space-time fractional Poisson processes by considering common random time-changes of a (finite-dimensional) vector of independent classical (non-fractional) Poisson processes. In some cases we also…

In this note, we provide and prove exact formulas for the mean and the trace of the covariance matrix of harmonic measure, regarded as a parametric probability distribution.

Numerous interesting properties in nonlinear systems analysis can be written as polynomial optimization problems with nonconvex sum-of-squares problems. To solve those problems efficiently, we propose a sequential approach of local…

We compute the sum and the alternating sum of the reciprocals of triangular numbers using two standard methods from calculus: a telescoping series approach and a power series approach. We then extend these results to generalized…

The partial sums of integer sequences that count the occurrences of a specific pattern in the binary expansion of positive integers have been investigated by different authors since the 1950s. In this note, we introduce generalized pattern…

We consider homogeneous random walks in the quarter-plane. The necessary conditions which characterize random walks of which the invariant measure is a sum of geometric terms are provided in [2,3]. Based on these results, we first develop…

We establish new pair correlation results for certain generic homogenous diagonal forms evaluated on the integers. Methods are analytic leading to explicit quantitative statements.

We consider the invariant measure of homogeneous random walks in the quarter-plane. In particular, we consider measures that can be expressed as a finite linear combination of geometric terms and present conditions on the structure of these…

The goal of this article is to prove the Sum of Squares Conjecture for real polynomials $r(z,\bar{z})$ on $\mathbb{C}^3$ with diagonal coefficient matrix. This conjecture describes the possible values for the rank of $r(z,\bar{z}) \|z\|^2$…

Explicit determinations of several classes of trigonometric sums are given. These sums can be viewed as analogues or generalizations of Gauss sums. In a previous paper, two of the present authors considered primarily sine sums associated…

It is shown that a separated sequence of points in the unit disc of the complex plane is in fact uniformly separated, if there exists a certain intermediate sequence whose separated subsequences are uniformly separated. This property is…

In this paper we will give a proof of a certain summation formula for Gamma functions utilizing Gegenbauer polynomials.

We study the linear span of commutators of free random variables and show that these are the only quadratic forms which satisfy the following equivalent properties: * preservation free infinite divisibility * free and strong cancellation of…

The exponential of the triangular matrix whose entries in the diagonal at distance $n$ from the principal diagonal are all equal to the sum of the inverse of the divisors of $n$ is the triangular matrix whose entries in the diagonal at…

We study large partial sums, localized with respect to the sums of variances, of a sequence of centered random variables. An application is given to the distribution of prime factors of typical integers.

The classical quadratic Gauss sum can be thought of as an exponential sum attached to a quadratic form on a cyclic group. We introduce an equivariant version of Gauss sum for arbitrary finite quadratic forms, which is an exponential sum…