Computing combinatorial decompositions of rings

Abstract

Using Buchberger's Gröbner basis theory, we obtain explicit algorithms for computing Stanley decompositions, Rees decompositions and Hironaka decompositions of commutative Noetherian rings. These decompositions are of considerable importance in combinatorics, in particular in the theory of Cohen-Macaulay complexes. We discuss several applications of our methods, including a new algorithm for finding primary and secondary invariants of finite group actions on polynomial rings.

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Research supported by the Institute for Mathematics and its Applications, Minneapolis, with funds provided by the National Science Foundation

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Sturmfels, B., White, N. Computing combinatorial decompositions of rings. Combinatorica 11, 275–293 (1991). https://doi.org/10.1007/BF01205079

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AMS subject classification (1980)

  • 68 C 20
  • 13-04
  • 20 C 05