TY - BOOK

T1 - Equivariant Gröbner bases and the Gaussian two-factor model

AU - Brouwer, A.E.

AU - Draisma, J.

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

UR - http://arxiv.org/pdf/0908.1530

M3 - Report

T3 - arXiv.org [math.AC]

BT - Equivariant Gröbner bases and the Gaussian two-factor model

PB - s.n.

ER -