Equivariant Syzygies of the Ideal of 2 x 2 Permanents of a 2 x n Matrix

We describe the equivariant syzygies of the ideal of $2\times 2$ permanents of a generic $2\times n$ matrix under its natural symmetric and torus group actions. Our proof gives us a new method of finding the Betti numbers of this ideal, which were first described by Gesmundo, Huang, Schenck, and Weyman.