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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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Published in: | Applicable algebra in engineering, communication and computing communication and computing, 2015-05, Vol.26 (6), p.507-525 |
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Main Author: | |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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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. |
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ISSN: | 0938-1279 1432-0622 |
DOI: | 10.1007/s00200-015-0263-6 |