The Face Lattice of Polyhedral Cones in the Theory of Cooperative Games

2018 ◽  
Author(s):  
Norman Lawrence Kleinberg
Keyword(s):  
Cooperative Games ◽  
Face Lattice ◽  
Polyhedral Cones ◽  
The Face

scholarly journals The face lattice of hyperplane arrangements

1988 ◽  
Vol 73 (1-2) ◽  
pp. 233-238 ◽  
Author(s):  
Günter M. Ziegler
Keyword(s):  
Hyperplane Arrangements ◽  
Face Lattice ◽  
The Face

Lawrence Polytopes

1990 ◽  
Vol 42 (1) ◽  
pp. 62-79 ◽  
Author(s):  
Margaret Bayer ◽  
Bernd Sturmfels
Keyword(s):  
Oriented Matroids ◽  
Oriented Matroid ◽  
Face Lattice ◽  
The Face

In 1980 Jim Lawrence suggested a construction Λ which assigns to a given rank r oriented matroid M on n points a rank n + r oriented matroid Λ(M) on 2n points such that the face lattice of Λ(M) is polytopal if and only if M is realizable. The Λ-construction generalized a technique used by Perles to construct a nonrational polytope [10]. It was used by Lawrence to prove that the class of polytopal lattices is strictly contained in the class of face lattices of oriented matroids (unpublished) and by Billera and Munson to show that the latter class is not closed under polarity. See [4] for a discussion of this construction and both of these applications.

On the Face Lattice of the Metric Polytope

2003 ◽  
pp. 118-128 ◽  
Author(s):  
Antoine Deza ◽  
Komei Fukuda ◽  
Tomohiko Mizutani ◽  
Cong Vo
Keyword(s):  
Face Lattice ◽  
The Face

scholarly journals Formalizing the Face Lattice of Polyhedra

2020 ◽  
pp. 185-203
Author(s):  
Xavier Allamigeon ◽  
Ricardo D. Katz ◽  
Pierre-Yves Strub
Keyword(s):  
Face Lattice ◽  
The Face

scholarly journals Computing the face lattice of a polytope from its vertex-facet incidences

2002 ◽  
Vol 23 (3) ◽  
pp. 281-290 ◽  
Author(s):  
Volker Kaibel ◽  
Marc E. Pfetsch
Keyword(s):  
Face Lattice ◽  
The Face

scholarly journals Complementation in the face lattice of a proper cone

1986 ◽  
Vol 79 ◽  
pp. 195-207 ◽  
Author(s):  
Raphael Loewy ◽  
Bit-Shun Tam
Keyword(s):  
Face Lattice ◽  
Proper Cone ◽  
The Face

The face lattice of ann-dimensional cube

1982 ◽  
Vol 14 (1) ◽  
pp. 82-86 ◽  
Author(s):  
Mary Katherine Bennett
Keyword(s):  
Face Lattice ◽  
The Face ◽  
Dimensional Cube
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