Inflation Algorithms for Positive and Principal Edge-bipartite Graphs and Unit Quadratic Forms

Authors:
Justyna Kosakowska
Affiliations:
(Correspd.) (Partially supported by Grant UMK 403-M) Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland, justus@mat.umk.pl
Venue:
Fundamenta Informaticae
Year:
2012

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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.