s-Hankel hypermatrices and 2 x 2 determinantal ideals

TL;DR

This paper introduces s-Hankel hypermatrices, explores associated determinantal ideals, describes their structure and primary decomposition, and provides geometric interpretations and generalizations of existing theorems.

Contribution

It generalizes Hankel matrices to s-Hankel hypermatrices and analyzes the structure and primary decomposition of related determinantal ideals.

Findings

Described the structure of the ideals I<s,t> and itilde{I}<s,t>

Provided explicit minimal primes for large s

Extended Watanabe's theorem to this new context

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.