Combinatorial invariance of Stanley-Reisner rings

Abstract

In this short note we show that Stanley—Reisner rings of simplicial complexes, which have had a “dramatic application” in combinatorics [2, p. 41], possess a rigidity property in the sense that they determine their underlying simplicial complexes.

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References

  1. 1.

    W. Bruns and J. Herzog, Cohen-Macaulay Rings.Cambridge Studies in Advanced Mathematics 39,Cambridge University Press,Cambridge, 1993.

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  2. 2.

    T. Hibi, Algebraic Combinatorics on Convex Polytopes.Carslaw Publications, 1992.

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Bruns, W., Gubeladze, J. Combinatorial invariance of Stanley-Reisner rings. Georgian Mathematical Journal 3, 315–318 (1996). https://doi.org/10.1007/BF02256722

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1991 Mathematics Subject Classification

  • 13F20

Key words and phrases

  • Simplicial complexes
  • Stanley-Reisner rings