2 x 2 permanental ideals of hypermatrices

Abstract

We study the structure of ideals generated by some classes of 2 \times 2 permanents of hypermatrices. This generalizes [9] on 2 x 2 permanental ideal of generic matrices. We compare the obtained structure to that of the corresponding determinantal ideals in [Swanson-Taylor 11]: while the notion of t-switchability introduced in [11] plays a role for both permanental and determinantal ideals, the permanents require further restrictions, which in general increases the number of minimal primes. In the last two section we examine a few related classes of permanental ideals. This is an extension of the first author's senior thesis at Reed College, 2011, under the second author's supervision.