Bar code for monomial ideals. (March 2019)

• Record Type: Journal Article
• Authors: Ceria, Michela
• Is Part Of: Journal of symbolic computation. Volume 91(2019)
• Page Start: 30
• Page End: 56
• Publication Date: 2019-03
• Subjects: (Strongly) stable ideals -- Integer partitions -- Determinantal formulas -- Pommaret basis; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2018.06.012
• Languages: English
• ISSNs: 0747-7171

Abstract

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.