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Bases in Systems of Simplices and Chambers
We consider a finite set of points in the -dimensional affine space
and two sets of objects that are generated by the set : the system
of -dimensional simplices with vertices in and the system of
chambers. The incidence matrix ,
, , induces the notion of linear
independence among simplices (and among chambers). We present an algorithm of
construction of bases of simplices (and bases of chambers). For the case
such an algorithm was described in the author's paper {\em Combinatorial bases
in systems of simplices and chambers} (Discrete Mathematics 157 (1996) 15--37).
However, the case of -dimensional space required a different technique. It
is also proved that the constructed bases of simplices are geometrical