1997/07/02 by Tatiana Alekseyevskaya, Alekseyevskaya, Tatiana
Computer Science · Engineering · #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Combinatorics (math.CO) #Digital Image Processing Techniques #FOS: Mathematics #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.math/9707218
openalex publication_date 1997/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a finite set E of points in the n-dimensional affine space and two sets of objects that are generated by the set E: the system Σ of n-dimensional simplices with vertices in E and the system Γ of chambers. The incidence matrix A= ∥ aσ, γ∥, σ∈ Σ, γ∈ Γ, 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 n=2 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 n-dimensional space required a different technique. It is also proved that the constructed bases of simplices are geometrical.