Related papers: An Euler-type formula for partitions of the M\"obi…
The Naruse hook-length formula is a recent general formula for the number of standard Young tableaux of skew shapes, given as a positive sum over excited diagrams of products of hook-lengths. In 2015 we gave two different $q$-analogues of…
We prove an Euler-Maclaurin formula for double polygonal sums and, as a corollary, we obtain approximate quadrature formulas for integrals of smooth functions over polygons with integer vertices. Our Euler-Maclaurin formula is in the spirit…
In the paper, the author elementarily unifies and generalizes eight identities involving the functions $\frac{\pm1}{e^{\pm t}-1}$ and their derivatives. By one of these identities, the author establishes two explicit formulae for computing…
This paper deals with a Euler type integral operator involving k-Mittag-Leffler function defined by Gupta and Parihar [8]. Furthermore, some special cases are also taken into consideration.
Weight-equitable partitions of graphs, which are a natural extension of the well-known equitable partitions, have been shown to be a powerful tool to weaken the regularity assumption in several well-known eigenvalue bounds. In this work we…
The purpose of this expository note is to give a proof of a Schur-type theorem that characterizes the inner functions in terms of their Taylor coefficients. In view of Beurling's theorem, this provides a sequential characterization of the…
Two semi-implicit Euler schemes for differential inclusions are proposed and analyzed in depth. An error analysis shows that both semi-implicit schemes inherit favorable stability properties from the differential inclusion. Their…
The closed-form expression for the quantum partition function of the improved Tietz oscillator is obtained using the Voronoi summation formula.
We study Dirichlet series enumerating orbits of Cartesian products of maps whose orbit distributions are modelled on the distributions of finite index subgroups of free abelian groups of finite rank. We interpret Euler factors of such orbit…
We solve the Dirichlet problem in the unit disc and derive the Poisson formula using very elementary methods and explore consequent simplifications in other foundational areas of complex analysis.
By using local and global versions of Bismut type derivative formulas, gradient estimates are derived for the Neumann semigroup on a narrow strip. Applications to functional/cost inequalities and heat kernel estimates are presented. Since…
The aim of this paper is to establish new inequalities for the Euler-Mascheroni by the continued fraction method.
We discuss the notion of the orbifold transform, and illustrate it on simple examples. The basic properties of the transform are presented, including transitivity and the exponential formula for symmetric products. The connection with the…
The purpose of this paper is to announce some new results on the structure of the higher order Euler-Lagrange mapping of the multiple-integral variational calculus on fibered manifolds,namely a description of its kernel and its image,and an…
We derive a general formula for the Euler characteristic of a fibration of projective hypersurfaces in terms of invariants of an arbitrary base variety. When the general fiber is an elliptic curve, such formulas have appeared in the physics…
We solve the problem of the computation of the orbifold Euler characteristics of $\Mbar_{g,n}$. We take the works of Harer-Zagier \cite{hz} and Bini-Harer \cite{bh} as our starting point, and apply the formalisms developed in \cite{wz} and…
In this paper, which is a complement of \cite{BG}, we study a few elementary invariants for configurations of skew lines, as introduced and analyzed first by Viro and his collaborators. We slightly simplify the exposition of some known…
We outline a method of calculation of partition functions of orientable manifolds with fluctuating metric and perform the calculation for the specific case of the unit interval.
An interplay between the Lambert series and Euler's Pentagonal Number Theorem gives an Euler-type recurrence relation for any given arithmetical function. As consequences of this, we present Euler-type recurrence relations for some…
E158 in the Enestrom index. Translation of the Latin original "Observationes analyticae variae de combinationibus" (1741). This paper introduces the problem of partitions, or partitio numerorum (the partition of integers). In the first part…