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Graphs of relations and Hilbert series
 Journal of Symbolic Computation
, 2007
"... Abstact We are discussing certain combinatorial and counting problems related to quadratic algebras. First we give examples which confirm the Anick conjecture on the minimal Hilbert series for algebras given by n generators and n(n−1) relations 2 for n � 7. Then we investigate combinatorial structur ..."
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Cited by 6 (5 self)
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Abstact We are discussing certain combinatorial and counting problems related to quadratic algebras. First we give examples which confirm the Anick conjecture on the minimal Hilbert series for algebras given by n generators and n(n−1) relations 2 for n � 7. Then we investigate combinatorial structure of colored graph associated to relations of RIT algebra. Precise descriptions of graphs (maps) corresponding to algebras with maximal Hilbert series are given in certain cases. As a consequence it turns out, for example, that RIT algebra may have a maximal Hilbert series only if components of the graph associated to each color are pairwise 2isomorphic.
On Preimages of Ideals in Certain Non–commutative Algebras
, 2003
"... In this paper we present new algorithms for non–commutative Gröbner ready algebras, which enable one to perform advanced operations with ideals and modules. In spite of the big interest in algorithmic treatment of related problems, preimage of ideal and central character decomposition were not disc ..."
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Cited by 5 (2 self)
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In this paper we present new algorithms for non–commutative Gröbner ready algebras, which enable one to perform advanced operations with ideals and modules. In spite of the big interest in algorithmic treatment of related problems, preimage of ideal and central character decomposition were not discussed before. An important algorithm for computation of the kernel of a homomorphism of left modules is described in the form, optimized for performance. We present these algorithms together with their implementation in computer algebra system Singular:Plural and detailed applications.
Computer Algebra System SINGULAR:PLURAL and noncommutative Groebner bases in theory and applications. Invited colloquium talk at
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