Alexander duality in subdivisions of Lawrence polytopes.
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Displaying 1 – 10 of 10
Bergman complexes, Coxeter arrangements, and graph associahedra.
Ardila, Federico, Reiner, Victor, Williams, Lauren (2005)
Séminaire Lotharingien de Combinatoire [electronic only]
Geometrically constructed bases for homology of partition lattices of types , and .
Björner, Anders, Wachs, Michelle L. (2004)
The Electronic Journal of Combinatorics [electronic only]
Integer partitions, tilings of -gons and lattices
Matthieu Latapy (2002)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
In this paper, we study two kinds of combinatorial objects, generalized integer partitions and tilings of -gons (hexagons, octagons, decagons, etc.). We show that the sets of partitions, ordered with a simple dynamics, have the distributive lattice structure. Likewise, we show that the set of tilings of a -gon is the disjoint union of distributive lattices which we describe. We also discuss the special case of linear integer partitions, for which other dynamical models exist.
Integer Partitions, Tilings of 2D-gons and Lattices
Matthieu Latapy (2010)
RAIRO - Theoretical Informatics and Applications
In this paper, we study two kinds of combinatorial objects, generalized integer partitions and tilings of 2D-gons (hexagons, octagons, decagons, etc.). We show that the sets of partitions, ordered with a simple dynamics, have the distributive lattice structure. Likewise, we show that the set of tilings of a 2D-gon is the disjoint union of distributive lattices which we describe. We also discuss the special case of linear integer partitions, for which other dynamical models exist.
Linear programming duality and morphisms
Winfried Hochstättler, Jaroslav Nešetřil (1999)
Commentationes Mathematicae Universitatis Carolinae
In this paper we investigate a class of problems permitting a good characterisation from the point of view of morphisms of oriented matroids. We prove several morphism-duality theorems for oriented matroids. These generalize LP-duality (in form of Farkas' Lemma) and Minty's Painting Lemma. Moreover, we characterize all morphism duality theorems, thus proving the essential unicity of Farkas' Lemma. This research helped to isolate perhaps the most natural definition of strong maps for oriented matroids....
On the combinatorial structure of arrangements of oriented pseudocircles.
Linhart, Johann, Ortner, Ronald (2004)
The Electronic Journal of Combinatorics [electronic only]
The active bijection between regions and simplices in supersolvable arrangements of hyperplanes.
Gioan, Emeric, Vergnas, Michel Las (2006)
The Electronic Journal of Combinatorics [electronic only]
The upper bound conjecture for arrangements of halfspaces.
Wesp, Gerhard (2001)
Beiträge zur Algebra und Geometrie
Unbounded regions in an arrangement of lines in the plane.
West, Alan (2004)
Beiträge zur Algebra und Geometrie
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