Related papers: On multi-symmetric functions and transportation po…
Following Talagrand's concentration results for permutations picked uniformly at random from a symmetric group [Tal95], Luczak and McDiarmid have generalized it to more general groups G of permutations which act suitably 'locally'. Here we…
We consider various inequalities for polynomials, with an emphasis on the most fundamental inequalities of approximation theory. In the sequel a key role is played by the generalized Minkowski functional \alpha(K,x), already being used by…
We study the commutation relations and normal ordering between families of operators on symmetric functions. These operators can be naturally defined by the operations of multiplication, Kronecker product, and their adjoints. As…
This is a hands on introduction to McMullen's Polytope Algebra. More than interesting on its own, this algebra was McMullen's tool to give a combinatorial proof of the g-theorem.
We construct a generalization of the multiplicative product of distributions presented by L. H\"ormander in [L. H\"ormander, {\it The analysis of linear partial differential operators I} (Springer-Verlag, 1983)]. The new product is defined…
Stanley generalized MacMahon's classical theorem by proving a product formula for the norm-trace generating function for plane partition with unbounded parts. In his recent work on biothorgonal polynomials, Kamioka proved a finite analogue…
We introduce the minor-closed, dual-closed class of multi-path matroids. We give a polynomial-time algorithm for computing the Tutte polynomial of a multi-path matroid, we describe their basis activities, and we prove some basic structural…
Although simplices are trivial from a linear optimization standpoint, the simplex algorithm can exhibit quite complex behavior. In this paper we study the behavior of max-slope pivot rules on (products of) simplices and describe the…
We study properties of arithmetic sets coming from multiplicative number theory and obtain applications in the theory of uniform distribution and ergodic theory. Our main theorem is a generalization of K\'atai's orthogonality criterion.…
In this paper, we study the formulae for a product of two product Euler polynomials. From this study, we derive some formulae for the integral of the product of two or more Ruler polynomials.
In this paper we investigate the multivariate orthogonal polynomials based on the theory of interacting Fock spaces. Our framework is on the same stream line of the recent paper by Accardi, Barhoumi, and Dhahri \cite{ABD}. The (classical)…
The purpose of this work is to analyse a family of mutually orthogonal polynomials on the unit ball with respect to an inner product which includes an additional term on the sphere. First, we will get connection formulas relating classical…
A form of Williamson's product theorem which applies to Williamson matrices of even order is presented.
This paper investigates summability principles for multilinear summing operators. The main result presents a novel inclusion theorem for a class of summing operators, which generalizes several classical results. As applications, we derive…
Two results on product of compact filters are shown to be the common principle behind a surprisingly large number of theorems.
We introduce a multivariate analogue of Bernoulli polynomials and give their fundamental properties: difference and differential relations, symmetry, explicit formula, inversion formula, multiplication theorem, and binomial type formula.…
We give a brief exposition of the proof of the Cayley-Salmon theorem and its recent role in incidence geometry. Even when we don't use the properties of ruled surfaces explicitly, the regime in which we have interesting results in…
We resolve affirmatively some conjectures of Reiner, Stanton, and White \cite{ReinerComm} regarding enumeration of transportation matrices which are invariant under certain cyclic row and column rotations. Our results are phrased in terms…
We provide a unifying interpretation of various optimal transport problems as a minimisation of a linear functional over the set of all Choquet representations of a given pair of probability measures ordered with respect to a certain convex…
We prove the existence of common hypercyclic, entire functions for certain families of translation operators.