Gröbner bases and statistics. (English) Zbl 0907.62087

Buchberger, Bruno (ed.) et al., Gröbner bases and applications. Based on a course for young researchers, January 1998, and the conference “33 years of Gröbner bases”, Linz, Austria, February 2–4, 1998. Cambridge: Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 251, 179-204 (1998).
In our writings we have pointed out that algebraic-geometric-combinatorial methods lead to solving problems in design and analysis of experiments and more specifically to fractional factorial designs. This paper is uses Gröbner Bases to attack problems in fractional factorial designs.
The contents of the paper are as follows: 1. Introduction. 2. Design of experiments to commutative algebra. 3. Computing confounding polynomials: the BM-algorithm. 4. Identifying the models. 5. Some problems: Problem 1: Given a fraction what are the models identifiable by it? Problem 2: Given a model which are the fractions which identify it? Problem 3: Which fractions identify the highest (lowest) number of models. 6. Concluding remarks.
All in all, a good reading for researchers in factorial designs.
For the entire collection see [Zbl 0883.00014].


62K15 Factorial statistical designs
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)