Details:
Title  Equivariant Grobner Bases and The Gaussian TwoFactor Models  Author(s)  Andries E. Brouwer, Jan Draisma  Type  Article in Journal  Abstract  Exploiting symmetry in Grobner basis computations is difficult when the symmetry takes the form of a group acting by automorphisms on
monomials in finitely many variables. This is largely due to the fact that the group elements, being invertible, cannot preserve a term order. By contrast, inspired by work of Aschenbrenner and Hillar, we introduce the concept of equivariant Grobner basis in a setting where a monoid acts by homomorphisms on monomials in potentially infinitely many variables. We require that the action be compatible with a term order, and under some further assumptions derive a Buchbergertype algorithm for computing equivariant Grobner bases.
Using this algorithm and the monoid of strictly increasing functions N → N
we prove that the kernel of the ring homomorphism
R[y_{ij}  i, j ∈ N, i > j] → R[s_{i} , t_{i}  i ∈ N], y_{ij} → s_{i} s_{j} t_{i} t_{j}
is generated by two types of polynomials: offdiagonal 3 × 3minors and pentads. This confirms a conjecture by Drton, Sturmfels, and Sullivant on the Gaussian twofactor model from algebraic statistics.
 Keywords  Equivariant Gröbner bases, algebraic factor analysis  Length  11  ISSN  10886842 
URL 
DOI: 10.1090/S002557182010024159 
Language  English  Journal  Mathematics of Computation  Publisher  American Mathematical Society  Year  2010  Month  September  Note  Electronically Published on September 9, 2010  Translation 
No  Refereed 
Yes 
