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Unimodular integer circulants associated with trinomials

Williams, G (2010) 'Unimodular integer circulants associated with trinomials.' International Journal of Number Theory, 6 (4). 869 - 876. ISSN 1793-0421

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Abstract

The n × n circulant matrix associated with the polynomial f(t)=∑di=0aiti (with d < n) is the one with first row (a0 ⋯ ad 0 ⋯ 0). The problem as to when such circulants are unimodular arises in the theory of cyclically presented groups and leads to the following question, previously studied by Odoni and Cremona: when is Res(f(t), tn-1) = ±1? We give a complete answer to this question for trinomials f(t) = tm ± tk ± 1. Our main result was conjectured by the author in an earlier paper and (with two exceptions) implies the classification of the finite CavicchioliHegenbarthRepovš generalized Fibonacci groups, thus giving an almost complete answer to a question of Bardakov and Vesnin. © 2010 World Scientific Publishing Company.

Item Type: Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Jim Jamieson
Date Deposited: 04 Jan 2012 11:49
Last Modified: 06 Jan 2020 16:15
URI: http://repository.essex.ac.uk/id/eprint/1810

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