Mariusz Felisiak

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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 [5], [13]), 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 [6]) of the root systems in the sense of Bourbaki [4], the mesh geometries &#x0393;(R<sub>&#x0394;</sub>, &#x03A6;<sub>A</sub>) of roots of &#x0394; in the sense of [20], and matrix morsifications A &#x2208; Mor<sub>&#x0394;</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 &#x0393;(R<sub>&#x0394;</sub>, &#x03A6;<sub>A</sub>) of roots of &#x0394; in the sense of [J. Pure Appl. Algebra, 215 (2010), 13-34], and matrix morsifications A &#x2208;(More)
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