On Face Vectors and Resolutions
2014 (English)Licentiate thesis, comprehensive summary (Other academic)
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.
Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2014. , ix, 21 p.
TRITA-MAT. MA, ISSN 1401-2278 ; 2014:07
IdentifiersURN: urn:nbn:se:kth:diva-145029ISBN: 978-91-7595-153-9OAI: oai:DiVA.org:kth-145029DiVA: diva2:715779
2014-05-30, Rum 3721, Matematik, Lindstedtsvägen 25, plan 7, KTH, Stockholm, 13:15 (English)
Welker, Volkmar, Professor
Björner, Anders, Professor
QC 201405132014-05-132014-05-062014-05-14Bibliographically approved
List of papers