<abstract xmlns="http://www.w3.org/1999/xhtml">Let <italic>K</italic> be a finite field. Let <italic>X</italic>* be a subset of the a ne space <italic>Kn</italic>, which is parameterized by odd cycles. In this paper we give an explicit Gröbner basis for the vanishing ideal, <bold>I</bold>(<italic>X</italic>*), of <italic>X</italic>*. We give an explicit formula for the regularity of <bold>I</bold>(<italic>X</italic>*) and finally if <italic>X</italic>* is parameterized by an odd cycle of length <italic>k</italic>, we show that the Hilbert function of the vanishing ideal of <italic>X</italic>* can be written as linear combination of Hilbert functions of degenerate torus.</abstract>

Let K be a finite field. Let X* be a subset of the a ne space Kn, which is parameterized by odd cycles. In this paper we give an explicit Gröbner basis for the vanishing ideal, I(X*), of X*. We give an explicit formula for the regularity of I(X*) and finally if X* is parameterized by an odd cycle of length k, we show that the Hilbert function of the vanishing ideal of X* can be written as linear combination of Hilbert functions of degenerate torus.

Vanishing Ideals Over Odd Cycles

Department of Mathematics, Escuela Superior de Física y Matemáticas

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Vanishing Ideals Over Odd Cycles"}

Let K be a finite field. Let X* be a subset of the a ne space Kn, which is parameterized by odd cycles. In this paper we give an explicit Gröbner basis for the...

Vanishing Ideals Over Odd Cycles

Published Online: Sep 26, 2019

Page range: 233 - 258

Received: Sep 12, 2018

Accepted: Oct 19, 2018

DOI: https://doi.org/10.2478/auom-2019-0029

Keywords
Toric set, Parameterized code, Hilbert function, Vanishing Ideal, Regularity index

© 2019 M. Eduardo Uribe-Paczka et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Vanishing Ideals Over Odd Cycles

Published Online: Sep 26, 2019

Page range: 233 - 258

Received: Sep 12, 2018

Accepted: Oct 19, 2018

DOI: https://doi.org/10.2478/auom-2019-0029

KeywordsToric set, Parameterized code, Hilbert function, Vanishing Ideal, Regularity index

© 2019 M. Eduardo Uribe-Paczka et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Toric set, Parameterized code, Hilbert function, Vanishing Ideal, Regularity index