Betti Numbers of Cut Ideals of Trees

  • Samu Potka Author University: Aalto University Author Department: Department of Mathematics and Systems Analysis
  • Camilo Sarmiento Author University: Max-Planck-Institute for Mathematics in the Sciences
Keywords: Betti numbers, cut ideals, tree graphs


Cut ideals, introduced by Sturmfels and Sullivant, are used in phylogenetics and algebraic
statistics. We study the minimal free resolutions of cut ideals of tree graphs. By employing
basic methods from combinatorial topology, we obtain upper bounds for the Betti numbers of this
type of ideals. These take the form of simple formulas on the number of vertices, which arise from
the enumeration of induced subgraphs of certain incomparability graphs associated to the edge
sets of trees.


Published Year: 2013
Volume: 4
Number: 1
Page Numbers: 108-117