Lattice path matroids: Structural properties

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jul 2006Embargo end date: 01 Jan 2004 Spain English Publisher:Elsevier BVJournal:European Journal of Combinatorics, volume 27, pages 701-738 (issn: 0195-6698,

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Authors: Joseph E. Bonin; Anna de Mier;

doi: 10.1016/j.ejc.2005.01.008 , 10.48550/arxiv.math/0403337

arXiv: math/0403337

handle: 2117/11878

Lattice path matroids: Structural properties

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Abstract

This paper studies structural aspects of lattice path matroids, a class of transversal matroids that is closed under taking minors and duals. 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.

34 pages, 15 figures

Country

Spain

Related Organizations

Universitat Polite`cnica de Catalunya
Spain
Universitat Politècnica de Catalunya
Spain
George Washington University
United States

Keywords

Combinatorial analysis, :05 Combinatorics::05B Designs and configurations [Classificació AMS], :Matemàtiques i estadística::Matemàtica discreta::Combinatòria [Àrees temàtiques de la UPC], Combinatorial aspects of matroids and geometric lattices, Matrius (Matemàtica), Classificació AMS::05 Combinatorics::05B Designs and configurations, Theoretical Computer Science, connected flats, Matroids, Lattice paths, Computational Theory and Mathematics, Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria, minors, circuits, FOS: Mathematics, Mathematics - Combinatorics, Geometry and Topology, Combinatorics (math.CO), 05B35, Anàlisi combinatòria

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