Patrik Nordbeck

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Polynomial composition is the operation of replacing the variables in a polynomial with other polynomials. In this paper we give a sufficient and necessary condition on a set Θ of polynomials to assure that the set F • Θ of composed polynomials is a SAGBI basis whenever F is.
Polynomial composition is the operation of replacing the variables in a polynomial with other polynomials. In this paper we give sufficient and necessary conditions on a set Y of non-commutative polynomials to assure that the set G + Y of composed polynomials is a Gro¨bner basis in the free asso-ciative algebra whenever G is. The subject was initiated by(More)
In this paper we introduce the concept of bi-automaton algebras, generalizing the automaton algebras previously defined by Ufnarovski. A bi-automaton algebra is a quotient of the free algebra, defined by a binomial ideal admitting a Gröbner basis which can be encoded as a regular set; we call such a Gröbner basis regular. We give several examples of(More)
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