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We show that the reduced mesh root systems and mesh geometries of roots for each of the simply-laced Dynkin diagrams can be classified by applying symbolic computer algebra computations and numeric algorithmic computations in Maple, C++ and Linux. Results of our computing experiences are presented in a table of Section 2 and in Section 6.
Extended Abstract 1 Preliminaries. Following the spectral graph theory, a graph coloring technique and algebraic methods in graph theory (see , ), we continue a Coxeter spectral study the category Bigr n of connected non-negative loop-free edge-bipartite (signed) graphs ∆, with n ≥ 1 vertices (bigraphs, in short), and their morsifications introduced… (More)
We continue and complete a Coxeter spectral study (presented in our talk given in SYNASC11, Timisoara, September 2011 ) of the root systems in the sense of Bourbaki , the mesh geometries Γ(R<sub>Δ</sub>, Φ<sub>A</sub>) of roots of Δ in the sense of , and matrix morsifications A ∈ Mor<sub>Δ</sub>, for… (More)
We continue and complete a Coxeter spectral study (presented in our talk given in SYNASC11 and SYNASC12) of the root systems in the sense of Bourbaki, the mesh geometries Γ(R<sub>Δ</sub>, Φ<sub>A</sub>) of roots of Δ in the sense of [J. Pure Appl. Algebra, 215 (2010), 13-34], and matrix morsifications A ∈… (More)