Journal Article10.3233/FI-2012-731
Inflation Algorithms for Positive and Principal Edge-bipartite Graphs and Unit Quadratic Forms
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TL;DR: In this paper, the authors describe combinatorial algorithms that compute the Dynkin type of any positive (resp. principal) unit quadratic form q : $\mathbb{N}$n → √ √ n$ and any positive edge-bipartite connected graph Δ.
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Abstract: We describe combinatorial algorithms that compute the Dynkin type (resp. Euclidean type) of any positive (resp. principal) unit quadratic form q : $\mathbb{N}$n → $\mathbb{N}$ and of any positive (resp. principal) edge-bipartite connected graph Δ. The study of the problem is inspired by applications of the algorithms in the representation theory, in solving a class of Diophantine equations, in the study of mesh geometries of roots, in the spectral analysis of graphs, and in the Coxeter-Gram classification of edge-bipartite graphs.
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A graph theoretical framework for the strong Gram classification of non-negative unit forms of Dynkin type A
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An Algorithmic-type Classification of Tetravalent One-regular Graphs Using Computer Algebra Tools
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A horizontal mesh algorithm for posets with positive Tits form
Mariusz Kaniecki,Justyna Kosakowska,Piotr Malicki,Grzegorz Marczak +3 more
- 31 Dec 2016
TL;DR: In this paper, the authors define a 2D-horizontal mesh algorithm that constructs a ~$\widehat{\Phi}_I$-mesh translation quiver such that it is isomorphic with the 2D Dynkin quiver.
References
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