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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W. Bruns and J. Herzog, Cohen-Macaulay Rings.Cambridge Studies in Advanced Mathematics 39,Cambridge University Press,Cambridge, 1993.
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
1991 Mathematics Subject Classification
Key words and phrases
- Simplicial complexes
- Stanley-Reisner rings