Stephen B. Maurer

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An interval in a graph is a JL tigraph induced 1) f all tire vertices an shortest paths between two given vertices. Intervals in matroid basis gr lphs satisfy many nice properties. Key recsults are: (1) any two vertices of a k :~is g~~aph i,re together in some longest interval; (2) every basis graph with :he minimum number of vertaces for its diametex is an(More)
A combinatorial pregeometry, or matroid, may be defined as a finite set of elements E and a collection of bases M, all subsets of E, such that for all B,B' G âiï and any é eB' — £, there exists e e B — B' for which B — e + e' e&. This exchange axiom suggests it is fruitful to represent a pregeometry Jt by a graph : Let there be a vertex for each basis and(More)
In this paper, we extend the notion of a circulant to a broader class of vertex.transitive graphs, which we call multidimensional circulants. This new class of graphs is shown to consist precisely of those vertex-transitive graphs with an automorphism group containing a regular abelian subgroup. The result is proved using a theorem of Sabidussi which shows(More)
The rank (resp. dimension) of a poset P is the cardinality of a largest (resp. smallest) set of linear orders such that its intersection is P and no proper subset has intersectior: P. Dimension has been studied extensively. Rank was introduced recently by Maurer and Rabinovitch in [4], where the rank of antichains was determined. In this paper we develop a(More)
Prospective audience: the course is intended for second and third year undergraduate students in Mathematics or Computer Science. Prerequisites: first year courses in mathematics, most notably Discrete Mathematics or Introduction to Combinatorics. Requirements and grade: Homeworks will be given once every two-three weeks; submitting at least three quarters(More)