Sara Faridi

Learn More
We generalize the concept of a cycle from graphs to simplicial complexes. We show that a simplicial cycle is either a sequence of facets connected in the shape of a circle, or is a cone over such a structure. We show that a simplicial tree is a connected cycle-free simplicial complex, and use this characterization to produce an algorithm that checks in(More)
Given a simple graph G on n vertices, we prove that it is possible to reconstruct several algebraic properties of the edge ideal from the deck of G, that is, from the collection of subgraphs obtained by removing a vertex from G. These properties include the Krull dimension, the Hilbert function, and all the graded Betti numbers i,j where j < n. We also(More)
2001 iv Acknowledgments I'd like to thank my advisor, Ira Gessel, for his unwavering support. He has been all that I ever could have asked for in an advisor, providing invaluable mathematical direction and allowing me the flexibility to deal with the rest of my life. Sara Billey and Susan Parker have not only agreed to sit on my committee, but have kept(More)
  • 1