A5040315652- Advanced Graph Theory Research
- graph theory and CDMA systems
- Advanced Combinatorial Mathematics
- Advanced Algebra and Logic
- Complexity and Algorithms in Graphs
- Limits and Structures in Graph Theory
- Graph Labeling and Dimension Problems
- semigroups and automata theory
- Finite Group Theory Research
- Computational Geometry and Mesh Generation
- Coding theory and cryptography
- Advanced Topics in Algebra
- Advanced Topology and Set Theory
- Commutative Algebra and Its Applications
- Graph theory and applications
- Data Management and Algorithms
- Rough Sets and Fuzzy Logic
- Interconnection Networks and Systems
- Advanced Differential Equations and Dynamical Systems
- Advanced Mathematical Identities
- Polynomial and algebraic computation
- Matrix Theory and Algorithms
- Optimization and Packing Problems
- Muon and positron interactions and applications
- Optimization and Search Problems
George Washington University
2010-2023
Queen Mary University of London
2022
United States Naval Academy
2022
Dartmouth College
1991-1994
University of Massachusetts Amherst
1994
We introduce the minor-closed, dual-closed class of multi-path matroids. give a polynomial-time algorithm for computing Tutte polynomial matroid, we describe their basis activities, and prove some basic structural properties. Key elements this work are two complementary perspectives develop these matroids: on one hand, matroids transversal that have special types presentations; other bases can be viewed as sets lattice paths in certain planar diagrams.
A result of Mason, as refined by Ingleton, characterizes transversal matroids the that satisfy a set inequalities relate ranks intersections and unions nonempty sets cyclic flats. We prove counterparts, for fundamental matroids, this other characterizations matroids. In particular, we show are precisely yield equality in Mason's deduce characterization due to Brylawski from simpler characterization.
J. Kahn and Kung showed how to reconstruct the group of a Dowling lattice. Here we show obtain lattice through techniques parallel those used in classical geometry field when coordinatizing projective or affine space. The analogy between lattices goes deeper. From an axiomatization rank four greater, first investigated [J. Bonin K. Bogart, Combin. Theory Ser. A56 (1991), 195-202], derive restriction Desargues′ theorem coordinate lines. In three, construction define works just as well for...
We provide evidence for five long-standing, basis-exchange conjectures matroids by proving them the enormous class of sparse paving matroids. also explore role that these may play in following problem: as a function size ground set, what is greatest number cyclic flats matroid can have?
Dowling lattices are a class of geometric lattices, based on groups, which have been shown to share many properties with projective geometries. In this paper we show that the automorphisms analogs We also treat similar results for several related lattices.