Lattice path matroids: Structural properties

This paper studies structural aspects of lattice path matroids. Among the basic topics treated are direct sums, duals, minors, circuits, and connected flats. One of the main results is a characterization of lattice path matroids in terms of fundamental flats, which are special connected flats from w...

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Bibliographic Details
Published in:European journal of combinatorics Vol. 27; no. 5; pp. 701 - 738
Main Authors: Bonin, Joseph E., de Mier, Anna
Format: Journal Article Publication
Language:English
Published: Elsevier Ltd 01.07.2006
Subjects:
05 Combinatorics
05B Designs and configurations
Anàlisi combinatòria
Classificació AMS
Combinatorial analysis
Combinatòria
Lattice paths
Matemàtica discreta
Matemàtiques i estadística
Matrius (Matemàtica)
Matroids
Àrees temàtiques de la UPC
05B35
primary
ISSN:0195-6698, 1095-9971
Online Access:Get full text
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Summary:This paper studies structural aspects of lattice path matroids. Among the basic topics treated are direct sums, duals, minors, circuits, and connected flats. One of the main results is a characterization of lattice path matroids in terms of fundamental flats, which are special connected flats from which one can recover the paths that define the matroid. We examine some aspects related to key topics in the literature of transversal matroids and we determine the connectivity of lattice path matroids. We also introduce notch matroids, a minor-closed, dual-closed subclass of lattice path matroids, and we find their excluded minors.
ISSN:0195-6698
1095-9971
DOI:10.1016/j.ejc.2005.01.008