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Article type: Research Article
Authors: Abarca, M. | Rivera, D.*; †
Affiliations: [a] Instituto de Investigación en Ciencias Básicas y Aplicadas Centro de Investigación en Ciencias Universidad Autónoma del Estado de Morelos Av. Universidad 1001, Cuernavaca, Mor. Mexico. {asma,darivera}@uaem.mx
Correspondence: [*] Address for correspondence: Centro de Investigación en Ciencias, Universidad Autónoma del Estado de Morelos; Av. Universidad 1001, Cuernavaca, Mor. Mexico.
Note: [†] The authors gratefully acknowledge the support of CONACyT (Grant 156667).
Abstract: A well known constructive proof for the 𝔸𝔻𝔼-classification of many mathematical objects, such as positive unit forms and their associated quasi-Cartan matrices, has lead to an Inflations Algorithm. However, this algorithm is not known to run in polynomial time. In this paper we use a so called flation transformation and show how its invariants can be used to characterize the Dynkin types 𝔸 and 𝔻 in the language of graph theory. Also, a polynomial-time algorithm for computing the Dynkin type is suggested.
Keywords: Positive unit forms, Dynkin-type, edge-bipartite graphs, combinatorial algorithms
DOI: 10.3233/FI-2016-1448
Journal: Fundamenta Informaticae, vol. 149, no. 3, pp. 241-261, 2016
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