Betti Numbers of Cut Ideals of Trees

Betti Numbers of Cut Ideals of Trees AS2012 Special Volume, part 2: This issue includes a second series of papers from talks, posters and collaborations resulting from and inspired by the Algebraic Statistics in the Alleghenies Conference at Penn State, which took place in July 2012. Potka, Samu Creator Faculty potka@kth.se Sarmiento, Camilo Creator MATH / Applied Mathematics Illinois Institute of Technology Affiliated department Betti numbers cut ideals tree graphs 2013 2013 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 topological combinatorics, 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. Article