Groebner bases and determinantal ideals

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We give an introduction to the theory of determinantal ideals and rings, their Groebner bases, initial ideals and algebras, respectively. The approach is based on the straightening law and the Knuth-Robinson-Schensted correspondence. The article contains a section treating the basic results about the passage to initial ideals and algebras.
58 pages The newest version has some typos corrected and uses the AMS style

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