Equivariant Gröbner bases and the Gaussian two-factor model

A.E. Brouwer, J. Draisma

Research output: Book/ReportReportAcademic

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Abstract

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.
Original languageEnglish
Publishers.n.
Number of pages14
Publication statusPublished - 2009

Publication series

NamearXiv.org [math.AC]
Volume0908.1530

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