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Quasi-stable ideals and Borel-fixed ideals with a given Hilbert polynomial

The present paper investigates properties of quasi-stable ideals and of Borel-fixed ideals in a polynomial ring k [ x 0 , ⋯ , x n ] , in order to design two algorithms: the first one takes as input n and an admissible Hilbert polynomial P ( z ), and outputs the complete list of saturated quasi-stabl...

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Bibliographic Details
Published in:Applicable algebra in engineering, communication and computing communication and computing, 2015-05, Vol.26 (6), p.507-525
Main Author: Bertone, Cristina
Format: Article
Language:English
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Summary:The present paper investigates properties of quasi-stable ideals and of Borel-fixed ideals in a polynomial ring k [ x 0 , ⋯ , x n ] , in order to design two algorithms: the first one takes as input n and an admissible Hilbert polynomial P ( z ), and outputs the complete list of saturated quasi-stable ideals in the chosen polynomial ring with the given Hilbert polynomial. The second algorithm has an extra input, the characteristic of the field k , and outputs the complete list of saturated Borel-fixed ideals in k [ x 0 , ⋯ , x n ] with Hilbert polynomial P ( z ). The key tool for the proof of both algorithms is the combinatorial structure of a quasi-stable ideal, in particular we use a special set of generators for the considered ideals, the Pommaret basis.
ISSN:0938-1279
1432-0622
DOI:10.1007/s00200-015-0263-6