Related papers: Plane partitions and their pedestal polynomials

This paper begins by extending the notion of a combinatorial configuration of points and lines to a combinatorial configuration of points and planes that we refer to as configurations of order $2$. We then proceed to investigate a further…

The aim of this paper is a quantitative analysis of the solution set of a system of polynomial nonlinear differential equations, both in the ordinary and partial case. Therefore, we introduce the differential counting polynomial, a common…

We will use different way (in this work) from the existing methods in the literature which speaking in the separation of convex sets was carried out by hyperplanes. We are examining the behavior of convex set which is the domain of convex…

We introduce and study the basic notion of polarized Poisson manifolds generalizing the classical case of Poisson manifolds and extend this last notion for the ${k-}$% symplectic stuctures. And also, we show that for any polarized…

The paper describes the algebraic structure of the graded algebra of differentially homogeneous polynomials of fixed finite order. We show that it is a finitely generated algebra, and we exhibit a minimal set of generators. Along the way,…

A partition polynomial is a refinement of the partition number p(n) whose coefficients count some special partition statistic. Just as partition numbers have useful asymptotics so do partition polynomials. In fact, their asymptotics…

This paper shows that the number of hooks of length k contained in all partitions of n equals k times the number of parts of length k in all partitions of n. It contains also formulas for the moments (under uniform distribution) of k-th…

We Define moments of partitions of integers, and show that they appear in higher order derivatives of certain combinations of functions.

Differential properties for orthogonal polynomials in several variables are studied. We consider multivariate orthogonal polynomials whose gradients satisfy some quasi--orthogonality conditions. We obtain several characterizations for these…

We classify homogeneous polynomials which split as powers of linear forms and whose polar map is birational.

Second-order polynomials generalize classical first-order ones in allowing for additional variables that range over functions rather than values. We are motivated by their applications in higher-order computational complexity theory,…

Using only a symmetric p-core partition and p-quotient, we give an explicit formula for the set of diagonal hook lengths of the associated symmetric partition.

We give a formula and an estimation for the number of irreducible polynomials in two (or more) variables over a finite field.

We prove the existence of Hall polynomials for prinjective representations of finite partially ordered sets of finite prinjective type. In Section 4 we shortly discuss consequences of the existence of Hall polynomials, in particular, we are…

We investigate which polynomials can possibly occur as factors in the denominators of rational solutions of a given partial linear difference equation (PLDE). Two kinds of polynomials are to be distinguished, we call them /periodic/ and…

We classify the polynomials with integral coefficients that, when evaluated on a group element of finite order $n$, define a unit in the integral group ring for infinitely many positive integers $n$. We show that this happens if and only if…

We define partially ample subvarieties of projective varieties, generalizing Ottem's work on ample subvarieties, and show their ubiquity. As an application, we obtain a connectedness result for pre-images of subvarieties by morphisms,…

The partitioning of space by hyperplanes in the context of discrete classification problem is considered. We obtain some relations for the number of partitions and establish a recurrence relation for the maximal number of partitions of R^n…

An overview of some recent results on the geometry of partial differential equations in application to integrable systems is given. Lagrangian and Hamiltonian formalism both in the free case (on the space of infinite jets) and with…

We define combinatorially a partial order on the set partitions and show that it is equivalent to the Bruhat-Chevalley-Renner order on the upper triangular matrices. By considering subposets consisting of set partitions with a fixed number…