Oleg Karpenkov
Published 2009-11-16Version 1
In this note we classify two-dimensional continued fractions for cubic irrationalities constructed by matrices with not large norm ($|*| \le 6$). The classification is based on the following new result: the class of matrices with an irreducible characteristic polynomial over the field of rational numbers is the class of matrices of frobenius type iff there exists an integer solution for a certain equation with integer coefficients.
Journal: Uspekhi Mat. Nauk 59 (2004), no. 5(359), 149--150; translation in Russian Math. Surveys 59 (2004), no. 5, 959--960
On tori triangulations associated with two-dimensional continued fractions of cubic irrationalities
Periodic representations for cubic irrationalities
Counting decomposable polynomials with integer coefficients
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