Bruhat intervals, polyhedral cones and Kazhdan-Lusztig-Stanley polynomials

1994 ◽  
Vol 215 (1) ◽  
pp. 223-236 ◽  
Author(s):  
M. J. Dyer
Keyword(s):  
Polyhedral Cones ◽  
Bruhat Intervals

On an application of the complex nonlinear complementarity problem

1976 ◽  
Vol 15 (1) ◽  
pp. 141-148 ◽  
Author(s):  
J. Parida ◽  
B. Sahoo
Keyword(s):  
Minimization Problem ◽  
Complementarity Problem ◽  
Complex Space ◽  
Nonlinear Complementarity Problem ◽  
Polyhedral Cone ◽  
Convex Minimization ◽  
Convex Minimization Problem ◽  
Polyhedral Cones ◽  
Existence Of A Solution ◽  
Nonlinear Complementarity

A theorem on the existence of a solution under feasibility assumptions to a convex minimization problem over polyhedral cones in complex space is given by using the fact that the problem of solving a convex minimization program naturally leads to the consideration of the following nonlinear complementarity problem: given g: Cn → Cn, find z such that g(z) ∈ S*, z ∈ S, and Re〈g(z), z〉 = 0, where S is a polyhedral cone and S* its polar.

On minimal positive basis for polyhedral cones in

2021 ◽  
pp. 1-17
Author(s):  
M. B. Alves ◽  
J. B. Gomes ◽  
K. M. Pedroso
Keyword(s):  
Polyhedral Cones ◽  
Positive Basis

scholarly journals Weak Generalized Lifting Property, Bruhat Intervals, and Coxeter Matroids

2020 ◽  
Author(s):  
Fabrizio Caselli ◽  
Michele D’Adderio ◽  
Mario Marietti
Keyword(s):  
Coxeter Group ◽  
Coxeter Groups ◽  
Combinatorial Properties ◽  
Coxeter Matroid ◽  
Finite Coxeter Group ◽  
Bruhat Intervals

Abstract We provide a weaker version of the generalized lifting property that holds in complete generality for all Coxeter groups, and we use it to show that every parabolic Bruhat interval of a finite Coxeter group is a Coxeter matroid. We also describe some combinatorial properties of the associated polytopes.

Characterizations of Fully Constrained Poses of Parallel Cable-Driven Robots: A Review

2008 ◽  
Author(s):  
Marc Gouttefarde
Keyword(s):  
Linear Algebra ◽  
Convex Cones ◽  
Mobile Platform ◽  
Polyhedral Cones ◽  
Fundamental Properties ◽  
Special Cases ◽  
Force Closure

The pose of the mobile platform of a parallel cable-driven robot is said to be fully constrained if any wrench can be created at the platform by pulling on it with the cables. A fully constrained pose is also known as a force-closure pose. In this paper, a review of three useful characterizations of a force-closure pose is proposed. These characterizations are stated in the form of theorems for which proofs are presented. Tools from linear algebra allow to derive some of these proofs while the others are more difficult and can hardly be obtained in this manner. Therefore, polyhedral cones, which are special cases of convex cones, are introduced along with some of their well-known fundamental properties. Then, it is shown how the aforementioned difficult proofs can be obtained as direct consequences of these properties.

scholarly journals From Bruhat intervals to intersection lattices and a conjecture of Postnikov

2009 ◽  
Vol 116 (3) ◽  
pp. 564-580 ◽  
Author(s):  
Axel Hultman ◽  
Svante Linusson ◽  
John Shareshian ◽  
Jonas Sjöstrand
Keyword(s):  
Bruhat Intervals

scholarly journals An Abstract Model for Bruhat Intervals

2000 ◽  
Vol 21 (2) ◽  
pp. 197-222 ◽  
Author(s):  
Fokko du Cloux
Keyword(s):  
Abstract Model ◽  
Bruhat Intervals
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