59,024 research outputs found
Intersections of sequences of ideals generated by polynomials
AbstractWe present a method for determining the reduced Gröbner basis with respect to a given admissible term order of order type ω of the intersection ideal of an infinite sequence of polynomial ideals.As an application we discuss the Lagrange type interpolation on algebraic sets and the “approximation” of the ideal I of an algebraic set by zero dimensional ideals, whose affine Hilbert functions converge towards the affine Hilbert function of I
Rigid Divisibility Sequences Generated by Polynomial Iteration
The goal of this thesis is to explore the properties of a certain class of sequences, rigid divisibility sequences, generated by the iteration of certain polynomials whose coefficients are algebraic integers. The main goal is to provide, as far as is possible, a classification and description of those polynomials which generate rigid divisibility sequences
Quasisymmetric harmonics of the exterior algebra
We study the ring of quasisymmetric polynomials in anticommuting
(fermionic) variables. Let denote the polynomials in anticommuting
variables. The main results of this paper show the following interesting facts
about quasisymmetric polynomials in anticommuting variables:
(1) The quasisymmetric polynomials in form a commutative sub-algebra of
.
(2) There is a basis of the quotient of by the ideal generated by
the quasisymmetric polynomials in that is indexed by ballot sequences.
The Hilbert series of the quotient is given by
where is the number of standard tableaux of shape
.
(3) There is a basis of the ideal generated by quasisymmetric polynomials
that is indexed by sequences that break the ballot conditionComment: 17 pages, changed list of authors, minor corrections to pape
- …