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AAA60: Workshop on General Algebra (60. Arbeitstagung Allgemeine Algebra)
June 22-25, 2000
Dresden University of Technology
Dresden, Germany

Organizers
Reinhard Pöschel, Manfred Droste, Bernhard Ganter

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The discrete convex combinations problem
by
A.G. Kolpakov
SibGUTI, Novosibirsk, Russia

Let Zn be a finite set; vi, i=1, ..., m, v are given vectors. Consider the following convex combinations problem (CCP): indicate all coefficients xi, i=1, ..., m of convex combinations of the vectors vi, i=1, ..., m giving the point v . The problem with additional condition: xi belongs to Zn is called the discrete CCP.

Using the representation of CCP general solution through the so-called “simplicial” solutions, we develop an algorithm constructing all solution of the discrete CCP. The algorithm constructs a tree, which branches correspond to solutions of the problem.

Date received: May 22, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caee-51.