2000/05/26 by Winfried Bruns, Bruns, Winfried, Aldo Conca +1
Computer Science · Mathematics · #13C40 #13F59 #14M12 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AC #math.AG #math.CO #msc:13C40 #msc:13F59 #msc:14M12
paper · pdf · doi:10.48550/arxiv.math/0005260
22 pages, uses epic, eepic
arxiv created 2000/05/26 · openalex publication_date 2000/05/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The first sections contain a survey of the application of the Knuth-Robinson-Schensted corerspondence to the computation of Groebner bases of determinantal ideals. We also set up a conceptual framework for this application in terms of so-called "KRS invariants". Then we show that the initial ideal of a determinantal ideal "defined by shape" is given by its KRS image. We furthermore characterize those among these ideals that even have a Groebner basis of products of minors, and show that they can be characterized in terms of Greene's KRS invariants. Furthermore it is shown that for the ideal generated by all t-minors the formation of initial ideal and symbolic power commutes. The last section contains a discussion of potential KRS invariants related to so-called 1-cogenerated ideals.