Toroidal Algorithms for Mesh Geometries of Root Orbits of the Dynkin Diagram D₄

• Autorzy: Simson D.
• Języki publikacji: EN

Abstrakty

EN

By applying symbolic and numerical computation and the spectral Coxeter analysis technique of matrix morsifications introduced in our previous paper [Fund. Inform. 124(2013)], we present a complete algorithmic classification of the rational morsifications and their mesh geometries of root orbits for the Dynkin diagram ₄ The structure of the isotropy group Gl(4, {Z})_D4 of D ₄ is also studied. As a byproduct of our technique we show that, given a connected loop-free positive edge-bipartite graph Δ, with n ≥ 4 vertices (in the sense of our paper [SIAM J. Discrete Math. 27(2013)]) and the positive definite Gram unit formqΔ ; Zⁿ→Z, any positive integer d ≥ 1 can be presented as d = qΔ(v), with v Є Zⁿ In case n = 3, a positive integer d ≥ 1 can be presented as d = qΔ(v), with v Є Zⁿ , if and only if d is not of the form 4^a(16 · b + 14), where a and b are non-negative integers.

Słowa kluczowe

EN

Coxeter spectrum; Dynkin diagram; edge-bipartite graph; inflation algorithm; matrix morsification; mesh geometry of root orbits; toroidal mesh algorithm; Weyl group

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2013
• Tom: Vol. 124, nr 3
• Strony: 339--364
• Opis fizyczny: Bibliogr. 44 poz., wykr.

Twórcy

autor

Simson D.

• Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

Bibliografia

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