2002/10/07 by Sara Faridi, Faridi, Sara · 1 citation
Mathematics · #13 (primary) #5 (secondary) #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.CO #msc:13 #msc:5
paper · pdf · doi:10.48550/arxiv.math/0210110
To appear in Manuscripta Mathematica
arxiv created 2002/10/07 · arxiv updated 2009/11/30
To a simplicial complex, we associate a square-free monomial ideal in the polynomial ring generated by its vertex set over a field. We study algebraic properties of this ideal via combinatorial properties of the simplicial complex. By generalizing the notion of a tree from graphs to simplicial complexes, we show that ideals associated to trees satisfy sliding depth condition, and therefore have normal and Cohen-Macaulay Rees rings. We also discuss connections with the theory of Stanley-Reisner rings.