Illinois Journal of Mathematics

The unimodality of pure $O$-sequences of type three in three variables

Bernadette Boyle

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Abstract

Since the 1970’s, great interest has been taken in the study of pure $O$-sequences, which are in bijective correspondence to the Hilbert functions of Artinian level monomial algebras. Much progress has been made in classifying these by their shape. It has been shown that all monomial complete intersections, Artinian algebras in two variables and Artinian level monomial algebras with type two in both three and four variables have unimodal Hilbert functions. This paper proves that Artinian level monomial algebras of type three in three variables have unimodal Hilbert functions. We will also discuss the licciness of these algebras.

Article information

Source
Illinois J. Math., Volume 58, Number 3 (2014), 757-778.

Dates
Received: 18 June 2014
Revised: 17 December 2014
First available in Project Euclid: 9 September 2015

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1441790389

Digital Object Identifier
doi:10.1215/ijm/1441790389

Mathematical Reviews number (MathSciNet)
MR3395962

Zentralblatt MATH identifier
1334.13014

Subjects
Primary: 13D40: Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series 13E10: Artinian rings and modules, finite-dimensional algebras
Secondary: 13C40: Linkage, complete intersections and determinantal ideals [See also 14M06, 14M10, 14M12] 13F20: Polynomial rings and ideals; rings of integer-valued polynomials [See also 11C08, 13B25] 05E40: Combinatorial aspects of commutative algebra

Citation

Boyle, Bernadette. The unimodality of pure $O$-sequences of type three in three variables. Illinois J. Math. 58 (2014), no. 3, 757--778. doi:10.1215/ijm/1441790389. https://projecteuclid.org/euclid.ijm/1441790389


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