The aim of this paper is to count 0-dimensional stable and strongly stable ideals in 2 and 3 variables, given their (constant) affine Hilbert polynomial p, by means of a bijection between these ideals and some integer partitions of p, which can be counted via determinantal formulas. This will be achieved by the Bar Code, a bidimensional diagram that allows to represent any finite set of terms M and desume many properties of the corresponding monomial ideal I, if M is an order ideal.
Bar code for monomial ideals / M. Ceria. - In: JOURNAL OF SYMBOLIC COMPUTATION. - ISSN 0747-7171. - 91:Special Issue(2019 Apr), pp. 30-56. [Epub ahead of print] ((Intervento presentato al 14. convegno MEGA2017 International Conference on Effective Methods in Algebraic Geometry : June, 12th – 16th tenutosi a Nizza nel 2017 [10.1016/j.jsc.2018.06.012].
Bar code for monomial ideals
M. Ceria
2019
Abstract
The aim of this paper is to count 0-dimensional stable and strongly stable ideals in 2 and 3 variables, given their (constant) affine Hilbert polynomial p, by means of a bijection between these ideals and some integer partitions of p, which can be counted via determinantal formulas. This will be achieved by the Bar Code, a bidimensional diagram that allows to represent any finite set of terms M and desume many properties of the corresponding monomial ideal I, if M is an order ideal.
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