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2016 $s$-Hankel hypermatrices and $2\times 2$ determinantal ideals
Alessio Sammartano
J. Commut. Algebra 8(2): 239-273 (2016). DOI: 10.1216/JCA-2016-8-2-239

Abstract

We introduce the concept of an $s$-Hankel hypermatrix, which generalizes both Hankel matrices and generic hypermatrices. We study two determinantal ideals associated to an $s$-Hankel hypermatrix: the ideal $\I {s}{t}$ generated by certain $2 \times 2$ slice minors, and the ideal $\It {s}{t}$ generated by certain $2 \times 2$ generalized minors. We describe the structure of these two ideals, with particular attention to the primary decomposition of $\I {s}{t}$, and provide the explicit list of minimal primes for large values of $s$. Finally we give some geometrical interpretations and generalize a theorem of Watanabe.

Citation

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Alessio Sammartano. "$s$-Hankel hypermatrices and $2\times 2$ determinantal ideals." J. Commut. Algebra 8 (2) 239 - 273, 2016. https://doi.org/10.1216/JCA-2016-8-2-239

Information

Published: 2016
First available in Project Euclid: 10 June 2016

zbMATH: 1348.13020
MathSciNet: MR3510920
Digital Object Identifier: 10.1216/JCA-2016-8-2-239

Subjects:
Primary: 13C40
Secondary: 13P10

Rights: Copyright © 2016 Rocky Mountain Mathematics Consortium

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Vol.8 • No. 2 • 2016
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