Illinois Journal of Mathematics
- Illinois J. Math.
- Volume 58, Number 3 (2014), 757-778.
The unimodality of pure $O$-sequences of type three in three variables
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.
Illinois J. Math., Volume 58, Number 3 (2014), 757-778.
Received: 18 June 2014
Revised: 17 December 2014
First available in Project Euclid: 9 September 2015
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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