We study the Gnedin–Kingman graph, which corresponds to Pieri’s rule for monomial basis {Mλ} in algebra QSym of quasisymmetric functions. The paper contains a detailed announcement results concerning classification indecomposable semifinite harmonic functions on graph. For these functions, we also establish multiplicativity property, is an analog Vershik–Kerov ring theorem.

i=0 aix , ai ∈ R. We will denote by πn the linear (vector) space of all such polynomials. The actual degree of p is the largest i for which ai is non-zero. The functions 1, x, . . . , x form a basis for πn, known as the monomial basis, and the dimension of the space πn is therefore n + 1. Bernstein polynomials are an alternative basis for πn, and are used to construct Bezier curves. The i-th Be...

Alexander duality has, in the past, made its way into commutative algebra through Stanley-Reisner rings of simplicial complexes. This has the disadvantage that one is limited to squarefree monomial ideals. The notion of Alexander duality is generalized here to arbitrary monomial ideals. It is shown how this duality is naturally expressed by Bass numbers, in their relations to the Betti numbers ...

K e y w o r d s E l l i p t i c PDEs, Generalized multiquadries, Different shape parameters. 1. I N T R O D U C T I O N The interest in meshfree methods to solve PDEs has grown considerably in the past 15 years. The two principal reasons are: (1) mesh generation over twoand three-dimensional complicated domains may require weeks or months to produce a well-behaved mesh, and (2) the convergence ...

In this paper we focus on Gröbner bases over rings for the univariate case. We identify a useful property of minimal Gröbner bases, that we call the " predictable leading monomial (PLM) property ". The property is stronger than " row reducedness " and is crucial in a range of applications. The first part of the paper is tutorial in outlining how the PLM property enables straightforward solution...

Quadratization is a transform of system ODEs with polynomial right-hand side into at most quadratic via the introduction new variables. It has been recently used as pre-processing step for model order reduction methods, so it important to keep number variables small. Several algorithms have designed search quadratization being monomials in original To understand limitations and potential ways i...

In this paper we provide algorithms for computing the bidiagonal decomposition of Wronskian matrices monomial basis polynomials and exponential polynomials. It is also shown that these can be used to perform accurately some algebraic computations with matrices, such as calculation their inverses, eigenvalues or singular values solutions linear systems. Numerical experiments illustrate results.

Due to the elimination property held by the lexicographic monomial order, the corresponding Gröbner bases display strong structural properties from which meaningful informations can easily be extracted. We study these properties for radical ideals of (co)dimension zero. The proof presented relies on a combinatorial decomposition of the finite set of points whereby iterated Lagrange interpolatio...

Let A be a Noetherian commutative ring with identity, let A[x] = A[x1, . . . , xn] be a polynomial ring over A, and let I ⊂ A[x] be an ideal. Geometrically, I defines a family of schemes over the base scheme SpecA; the fiber over each point p ∈ SpecA is a subscheme of the affine space Ank(p) = Speck(p)[x], where k(p) = Ap/pp is the residue field of p. Let > be a total order on the monomials of ...

Linear algebra is introduced by Faugère in F4 to speed up the reduction procedure during Gröbner basis computations. Linear algebra has also been used in fast implementations of F5 and other signature-based Gröbner basis algorithms. To use linear algebra for reductions, an important step is constructing matrices from critical pairs and existing polynomials by the Symbolic Preprocessing function...