gale transform
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2016 ◽  
Vol 73 (1) ◽  
pp. 281-304
Author(s):  
Daniel J. Bates ◽  
Jonathan D. Hauenstein ◽  
Matthew E. Niemerg ◽  
Frank Sottile
Keyword(s):  




2014 ◽  
Vol 2 ◽  
Author(s):  
SOPHIE MORIER-GENOUD ◽  
VALENTIN OVSIENKO ◽  
RICHARD EVAN SCHWARTZ ◽  
SERGE TABACHNIKOV

AbstractWe study the space of linear difference equations with periodic coefficients and (anti)periodic solutions. We show that this space is isomorphic to the space of tame frieze patterns and closely related to the moduli space of configurations of points in the projective space. We define the notion of a combinatorial Gale transform, which is a duality between periodic difference equations of different orders. We describe periodic rational maps generalizing the classical Gauss map.



2012 ◽  
Vol 312 (3) ◽  
pp. 647-651 ◽  
Author(s):  
Antonio Cossidente ◽  
Angelo Sonnino


2010 ◽  
Vol 310 (22) ◽  
pp. 3206-3210 ◽  
Author(s):  
Antonio Cossidente ◽  
Angelo Sonnino


2008 ◽  
Vol 319 (8) ◽  
pp. 3120-3127 ◽  
Author(s):  
Susan M. Cooper ◽  
Steven P. Diaz
Keyword(s):  


2002 ◽  
Vol 340 (1-3) ◽  
pp. 149-154 ◽  
Author(s):  
Abdo Y. Alfakih ◽  
Henry Wolkowicz


2000 ◽  
Vol 230 (1) ◽  
pp. 127-173 ◽  
Author(s):  
David Eisenbud ◽  
Sorin Popescu


1970 ◽  
Vol 22 (2) ◽  
pp. 265-287 ◽  
Author(s):  
P. McMullen ◽  
G. C. Shephard

During the last few years, Branko Grünbaum, Micha Perles, and others have made extensive use of Gale transforms and Gale diagrams in investigating the properties of convex polytopes. Up to the present, this technique has been applied almost entirely in connection with combinatorial and enumeration problems. In this paper we begin by showing that Gale transforms are also useful in investigating properties of an essentially metrical nature, namely the symmetries of a convex polytope. Our main result here (Theorem (10)) is that, in a manner that will be made precise later, the symmetry group of a polytope can be represented faithfully by the symmetry group of a Gale transform of its vertices. If a d-polytope P ⊂ Ed has an axis of symmetry A (that is, A is a linear subspace of Ed such that the reflection in A is a symmetry of P), then it is called axi-symmetric. Using Gale transforms we are able to determine, in a simple manner, the possible numbers and dimensions of axes of symmetry of axi-symmetric polytopes.



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