s-Hankel hypermatrices and 2 x 2 determinantal ideals
arXiv:1210.4230 · doi:10.1216/JCA-2016-8-2-239
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<s,t> generated by certain 2 x 2 slice minors, and the ideal \tilde{I}<s,t> 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<s,t>, 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.