Bernstein, David; Zelevinsky, Andrei Combinatorics of maximal minors. (English) Zbl 0794.13021 J. Algebr. Comb. 2, No. 2, 111-121 (1993). In this paper the authors continue [see B. Sturmfels and A. Zelevinsky, Adv. Math. 98, No. 1, 65-112 (1993; Zbl 0776.13009)], the study of the Newton polytope of the product of all maximal minors of an \(m\times n\)-matrix of indeterminates. They prove some of the conjectures made in the paper cited above, and get as a consequence: The set of all maximal minors of a generic \(m \times n\)-matrix \(X=(x_{ij})\) is a universal Gröbner basis for the ideal generated by them in the polynomial ring \(\mathbb{C} [x_{ij}]\). This paper is essentially self contained, but the results and methods are mostly combinatorial. Reviewer: M.Morales (Saint-Martin-d’Heres) Cited in 2 ReviewsCited in 16 Documents MSC: 13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) 05B35 Combinatorial aspects of matroids and geometric lattices 15A15 Determinants, permanents, traces, other special matrix functions 14M25 Toric varieties, Newton polyhedra, Okounkov bodies Keywords:matching field; Newton polytope; maximal minors; Gröbner basis PDF BibTeX XML Cite \textit{D. Bernstein} and \textit{A. Zelevinsky}, J. Algebr. Comb. 2, No. 2, 111--121 (1993; Zbl 0794.13021) Full Text: DOI References: [1] Sturmfels, B.; Zelevinsky, A., Maximal minors and their leading terms, Advances in Math, 98, 65-112, (1993) · Zbl 0776.13009 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.