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Unimodular integer circulants associated with trinomials

Williams, G (2010) 'Unimodular integer circulants associated with trinomials.' International Journal of Number Theory, 06 (04). pp. 869-876. ISSN 1793-0421


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The n � n circulant matrix associated with the polynomial [image removed] (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 Cavicchioli?Hegenbarth?Repov? generalized Fibonacci groups, thus giving an almost complete answer to a question of Bardakov and Vesnin.

Item Type: Article
Uncontrolled Keywords: Unimodular matrices; circulants; resultants
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health
Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 04 Jan 2012 11:49
Last Modified: 06 Jan 2022 13:27

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