We determine the infinite sequences (ak) of integers that can be generated by polynomials with integral coefficients, in the sense that for each finite initial segment of length n there is an integral polynomial fn(x) of degree < n such that ak = fn(k) for k = 0, 1, . . . , n − 1. Let P be the set of such sequences and Π the additive group of all infinite sequences of integers. Then P is a subg...

We introduce the Macaulay2 package BooleanGB, which computes a Gröbner basis for Boolean polynomials using a binary representation rather than symbolic. We compare the runtime of several Boolean models from systems in biology and give an application to Sudoku.

This paper presents discrete Galerkin method for obtaining the numerical solution of higher even-order integro-differential equations with variable coefficients. We use the generalized Jacobi polynomials with indexes corresponding to the number of homogeneous initial conditions as natural basis functions for the approximate solution. Numerical results are presented to demonstrate the effectiven...

in this paper, the ritz-galerkin method in bernstein polynomial basis is applied for solving the nonlinear problem of the magnetohydrodynamic (mhd) flow of third grade fluid between the two plates. the properties of the bernstein  polynomials together with the ritz-galerkin method are used to reduce the solution of the mhd couette flow of non-newtonian fluid in a porous medium to the solution o...

Abstract Subword complexes were defined by Knutson and Miller in 2004 to describe Gröbner degenerations of matrix Schubert varieties. a certain type are called pipe dream complexes. The facets such complex indexed dreams, or, equivalently, monomials the corresponding polynomial. In 2017 Assaf Searles basis slide polynomials, generalizing Stanley symmetric functions, described combinatorial rule...

Gröbner basis detection (GBD) is defined as follows: given a set of polynomials, decide whether there exists and if “yes” find a term order such that the set of polynomials is a Gröbner basis. This problem was proposed by Gritzmann and Sturmfels (1993) and it was shown to be NP-hard by Sturmfels and Wiegelmann. We investigate the computational complexity of this problem when the given set of po...

The Bernstein operator Bn for a simplex in Rd is naturally defined via the Bernstein basis obtained from the barycentric coordinates given by its vertices. Here we consider a generalisation of this basis and the Bernstein operator, which is obtained from generalised barycentric coordinates that are given for more general configurations of points in Rd . We call the associated polynomials a Bern...

The irreducible representations of symmetric groups can be realized as certain graded pieces invariant rings, equivalently global sections line bundles on partial flag varieties. There are various ways to choose useful bases such Specht modules Sλ. Particularly powerful web bases, which make important connections with cluster algebras and quantum link invariants. Unfortunately, only known in ve...