12 citations · 13 across the 3 of their papers we have counts for
5 papers
Exponential Genus Problems in one-relator products of groups
Andrew J. Duncan
Exponential equations in free groups were studied initially by Lyndon and Schutzenberger and then by Comerford and Edmunds. Comerford and Edmunds showed that the problem of determi…
Centraliser Dimension and Universal Classes of Groups
A. J. Duncan, I. V. Kazatchkov, V. N. Remeslennikov
In this paper we establish results that will be required for the study of the algebraic geometry of partially-commutative groups. We define classes of groups axiomatised by sentenc…
Extending the Promise of the Deutsch--Jozsa--Hoyer Algorithm for Finite Groups
Michael Batty, Samuel L. Braunstein, Andrew J. Duncan
Hoyer has given a generalisation of the Deutsch--Jozsa algorithm which uses the Fourier transform on a group G which is (in general) non-Abelian. His algorithm distinguishes betwee…
Quantum algorithms in group theory
Michael Batty, Samuel L. Braunstein, Andrew J. Duncan +1
We present a survey of quantum algorithms, primarily for an intended audience of pure mathematicians. We place an emphasis on algorithms involving group theory.
Word Hyperbolic Semigroups
Andrew Duncan, Robert H. Gilman
The study of word hyperbolic groups is a prominent topic in geometric group theory; however word hyperbolic groups are defined by a geometric condition which does not extend natura…