Williams, G (2010) Unimodular integer circulants associated with trinomials. International Journal of Number Theory, 06 (04). pp. 869-876. DOI https://doi.org/10.1142/s1793042110003289
Williams, G (2010) Unimodular integer circulants associated with trinomials. International Journal of Number Theory, 06 (04). pp. 869-876. DOI https://doi.org/10.1142/s1793042110003289
Williams, G (2010) Unimodular integer circulants associated with trinomials. International Journal of Number Theory, 06 (04). pp. 869-876. DOI https://doi.org/10.1142/s1793042110003289
Abstract
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 |
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Uncontrolled Keywords: | Unimodular matrices; circulants; resultants |
Subjects: | Q Science > QA Mathematics |
Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematics, Statistics and Actuarial Science, School of |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 04 Jan 2012 11:49 |
Last Modified: | 16 May 2024 18:30 |
URI: | http://repository.essex.ac.uk/id/eprint/1810 |
Available files
Filename: UnimodularIntCirculants.pdf