Related papers: A combinatorial identity for studying Sato-Tate ty…

In this paper we give a convolution identity for the complete and elementary symmetric functions. This result can be used to proving and discovering some combinatorial identities involving $r$-Stirling numbers, $r$-Whitney numbers and…

In 1984, Bressoud and Subbarao obtained an interesting weighted partition identity for a generalized divisor function, by means of combinatorial arguments. Recently, the last three named authors found an analytic proof of the aforementioned…

Dirac delta function (delta-distribution) approach can be used as efficient method to derive identities for number series and their reciprocals. Applying this method, a simple proof for identity relating prime counting function…

The union of a collection of $n$ sets is generally expressed in terms of a characteristic (indicator) function that contains $2^{n}-1$ terms. In this article, a much simpler expression is found that requires the evaluation of $n$ terms…

This note presents a simple proof of the characteristic function of Student's $t$-distribution. The method of proof, which involves finding a differential equation satisfied by the characteristic function, is applicable to many other…

In this paper, we consider forward and inverse problems for subdiffusion equations with time-dependent coefficients. The fractional derivative is taken in the sense of Riemann-Liouville. Using the classical Fourier method, the theorem of…

Let L be a bounded distributive lattice. We give several characterizations of those L^n --> L mappings that are polynomial functions, i.e., functions which can be obtained from projections and constant functions using binary joins and…

In this article, we introduce combinatorial models for poly-Bernoulli polynomials and poly-Euler numbers of both kinds. As their applications, we provide combinatorial proofs of some identities involving poly-Bernoulli polynomials.

The author uses a Stein-type covariance identity to obtain moment estimators for the parameters of the quadratic polynomial subfamily of Pearson distributions. The asymptotic distribution of the estimators is obtained, and normality and…

We prove the Sato--Tate distribution of Kloosterman sums over function fields with explicit error terms, when the places vary in arithmetic progressions or short intervals. A joint Sato--Tate distribution of two ``different" exponential…

Lapid and Mao formulated a conjecture on an explicit formula of Whittaker Fourier coefficients of automorphic forms on quasi-split classical groups and metaplectic groups as an analogue of Ichino-Ikeda conjecture. They also showed that this…

Event-by-event fluctuations of the chemical composition of the hadronic final state of relativistic heavy-ion collisions carry valuable information on the properties of strongly interacting matter produced in the collisions. However, in…

Let X be a locally compact Abelian group. We consider linear forms of independent random variables with values in X. In doing so, one of the coefficients of the linear forms is a random variable with a Bernoulli distribution. For some…

This work deals with a new generalization of $r$-Stirling numbers using $l$-tuple of permutations and partitions called $(l,r)$-Stirling numbers of both kinds. We study various properties of these numbers using combinatorial interpretations…

Fractals equipped with intrinsic arithmetic lead to a natural definition of differentiation, integration and complex numbers. Applying the formalism to the problem of a Fourier transform on fractals we show that the resulting transform has…

We are often interested in decomposing complex, structured data into simple components that explain the data. The linear version of this problem is well-studied as dictionary learning and factor analysis. In this work, we propose a…

Modern applications of algebraic topology to point cloud data analysis have motivated active investigation of combinatorial clique complexes -- high-dimensional extensions of combinatorial graphs. We show that meaningful invariants of such…

In this paper, we consider polynomials associated with faces and internal quadrilaterals of a cuboctahedron and classify them under the requirement that they are consistent. These polynomials give rise to a system of partial difference…

Some applications of a result, which is proved recently, is considered. We first prove three determinantal identities concerning the binomial coefficient and Stirling numbers of the first and the second kind. We also easily obtain the…

Recently Andrews and Bachraoui proved identities relating certain restricted partitions into distinct even parts with restricted 4-regular partitions by the theory of basic hypergeometric series. They also posed a question regarding…