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Chordal and Complete Structures in Combinatorics and Commutative Algebra
Stockholm University, Faculty of Science, Department of Mathematics.
2010 (English)Doctoral thesis, monograph (Other academic)
Abstract [en]

This thesis is divided into two parts. The first part is concerned with the commutative algebra of certain combinatorial structures arising from uniform hypergraphs. The main focus lies on two particular classes of hypergraphs called chordal hypergraphs and complete hypergraphs, respectively. Both these classes arise naturally as generalizations of the corresponding well known classes of simple graphs. The classes of chordal and complete hypergraphs are introduced and studied in Chapter 2 and Chapter 3 respectively. Chapter 4, that is the content of \cite{E5}, answers a question posed at the P.R.A.G.MAT.I.C. summer school held in Catania, Italy, in 2008. In Chapter 5 we study hypergraph analogues of line graphs and cycle graphs. Chapter 6 is concerned with a connectedness notion for hypergraphs and in Chapter 7 we study a weak version of shellability.The second part is concerned with affine monoids and their monoid rings. Chapter 8 provide a combinatorial study of a class of positive affine monoids that behaves in some sense like numerical monoids. Chapter 9 is devoted to the class of numerical monoids of maximal embedding dimension. A combinatorial description of the graded Betti numbers of the corresponding monoid rings in terms of the minimal generators of the monoids is provided. Chapter 10 is concerned with monomial subrings generated by edge sets of complete hypergraphs.

Place, publisher, year, edition, pages
Stockholm: Department of Mathematics, Stockholm University , 2010. , 105 p.
Keyword [en]
Betti numbers, chordal hypergraphs, complete hypergraphs, hypercycle, line hypergraph, numerical monoids, positive affine monoids
National Category
Other Mathematics
Research subject
URN: urn:nbn:se:su:diva-48241ISBN: 978-91-7447-195-3OAI: diva2:374550
Public defence
2011-01-18, sal 14, hus 5, Kräftriket, Roslagsvägen 101, Stockholm, 13:00 (English)
Available from: 2010-12-27 Created: 2010-12-06 Last updated: 2014-06-17Bibliographically approved

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