On the computation of Hilbert series and Poincare series for algebras with infinite Grobner bases

Hilbert Series of Group Representations and Grbner Bases for Generic Modules

Each matrix representation P: G —> GLn(K) of a finite Group G over a field K induces an action of G on the module A over the polynomial algebra A = K [ x 1 , . . . , xn]. The graded A-submodule M(P) of A generated by the orbit of (x1, ..., xn) is studied. A decomposition of MO) into generic modules is given. Relations between the numerical invariants of P and those of M(P), the latter being eff...

Sets of Hilbert Series and Their Applications

We consider graded finitely presented algebras and modules over a field. Under some restrictions, the set of Hilbert series of such algebras (or modules) becomes finite. Claims of that types imply rationality of Hilbert and Poincare series of some algebras and modules, including periodicity of Hilbert functions of common (e.g., Noetherian) modules and algebras of linear growth.

The Hilbert-poincare Series for Some Algebras of Invariant of Cyclic Groups

New explicit and Soliton Wave Solutions of Some Nonlinear Partial Differential Equations with Infinite Series Method

To start with, having employed transformation wave, some nonlinear partial differential equations have been converted into an ODE. Then, using the infinite series method for equations with similar linear part, the researchers have earned the exact soliton solutions of the selected equations. It is required to state that the infinite series method is a well-organized method for obtaining exact s...

Noncommutative Grobner basis, Hilbert series, Anick's resolution and BERGMAN under MS-DOS

The definition and main results connected with Gröbner basis, Hilbert series and Anick's resolution are formulated. The method of the infinity behavior prediction of Gröbner basis in noncommu-tative case is presented. The extensions of BERGMAN package for IBM PC compatible computers are described. Let A =< X|R > be a finitely presented associative algebra over field K. Here are the main example...