On Face Vectors and Resolutions

• Main Author: Goodarzi, Afshin
• Format: Others
• Language: English
• Published: KTH, Matematik (Avd.) 2014
• Online Access: http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-145029; http://nbn-resolving.de/urn:isbn:978-91-7595-153-9

This thesis consist of the following three papers. Convex hull of face vectors of colored complexes. In this paper we verify a conjecture by Kozlov (Discrete ComputGeom18(1997) 421–431), which describes the convex hull of theset of face vectors ofr-colorable complexes onnvertices. As partof the proof we derive a generalization of Turán’s graph theorem. Cellular structure for the Herzog–Takayama Resolution. Herzog and Takayama constructed explicit resolution for the ide-als in the class of so called ideals with a regular linear quotient.This class contains all matroidal and stable ideals. The resolu-tions of matroidal and stable ideals are known to be cellular. Inthis note we show that the Herzog–Takayama resolution is alsocellular. Clique Vectors ofk-Connected Chordal Graphs. The clique vectorc(G)of a graphGis the sequence(c1,c2,...,cd)inNd, whereciis the number of cliques inGwithivertices anddis the largest cardinality of a clique inG. In this note, we usetools from commutative algebra to characterize all possible cliquevectors ofk-connected chordal graphs. === <p>QC 20140513</p>