We show that the kernel I of the ring homomorphism R[yij | I, j ¿ N, i > j] ¿ R[si, ti | i ¿ N] determined by yij ¿ sisj +titj is generated by two types of polynomials: off-diagonal 3 x 3-minors and pentads. This confirms a conjecture by Drton, Sturmfels, and Sullivant on the Gaussian two-factor model. Our proof is computational: inspired by work of Aschenbrenner and Hillar we introduce the concept of G-Gröbner basis, where G is a monoid acting on an infinite set of variables, and we report on a computation that yielded a finite G-Gröbner basis of I relative to the monoid G of strictly increasing functions N ¿ N.
|Number of pages||14|
|Publication status||Published - 2009|