• Corpus ID: 233407515

Random subcomplexes and Betti numbers of random edge ideals

  title={Random subcomplexes and Betti numbers of random edge ideals},
  author={Anton Dochtermann and Andrew Newman},
We study homological properties of random quadratic monomial ideals in a polynomial ring R = K[x1, . . . xn], utilizing methods from the Erdős–Rényi model of random graphs. Here for a graph G ∼ G(n,p) we consider the ‘coedge’ ideal IG corresponding to the missing edges of G, and study Betti numbers of R/IG as n tends to infinity. Our main results involve fixing the edge probability p = p(n) so that asymptotically almost surely the Krull dimension of R/IG is fixed. Under these conditions we… 

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