Details:
Title  Equivariant Gr\"obner bases and the Gaussian twofactor model.  Author(s)  Brouwer Andries E., Jan Draisma  Type  Article in Journal  Abstract  Exploiting symmetry in Gröbner 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 Gröbner 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 Gröbner bases.
Using this algorithm and the monoid of strictly increasing functions $ \mathbb{N} \to \mathbb{N}$ we prove that the kernel of the ring homomorphism
$\displaystyle \mathbb{R}[y_{ij} \mid i,j \in \mathbb{N}, i > j] \to\mathbb{R}[s_i,t_i \mid i \in \mathbb{N}], y_{ij} \mapsto s_is_j + t_it_j $
is generated by two types of polynomials: offdiagonal $ 3 \times 3$minors and pentads. This confirms a conjecture by Drton, Sturmfels, and Sullivant on the Gaussian twofactor model from algebraic statistics.  See more at: http://www.ams.org/journals/mcom/201180274/S002557182010024159/home.html#sthash.Lwuz1DXE.dpuf  ISSN  00255718; 10886842/e 
File 
 URL 
http://www.ams.org/journals/mcom/201180274/S002557182010024159/home.html 
Language  English  Journal  Math. Comput.  Volume  80  Number  274  Pages  11231133  Publisher  American Mathematical Society (AMS), Providence, RI  Year  2011  Edition  0  Translation 
No  Refereed 
No 
