s-Hankel hypermatrices and 2 x 2 determinantal ideals

Alessio Sammartano

doi:10.1216/jca-2016-8-2-239

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arXiv · 1210.4230

s-Hankel hypermatrices and 2 x 2 determinantal ideals

Alessio Sammartano

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Abstract

We introduce the concept of 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 generated by certain 2 x 2 slice minors, and the ideal \tilde{I} generated by certain 2 x 2 generalized minors. We describe the structure of these two ideals, with particular attention to the primary decomposition of I , and provide the explicit list of minimal primes for large values of s. Finally we give some geometrical interpretations and generalise a theorem of Watanabe.

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BibTeX RIS

Alessio Sammartano. 2012-10-16. s-Hankel hypermatrices and 2 x 2 determinantal ideals. https://doi.org/10.1216/jca-2016-8-2-239

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