Publications in Refereed Journals
'Epis are onto for generalised inverse semigroups', Semigroup Forum, Vol. 23, 255-259, 1981.
'The determination of all absolutely closed varieties of semigroups', Proc. Amer. Math. Soc., Vol. 87, 419-421, 1983.
'The varieties of commutative semigroups for which epis are onto', Proc. Roy. Edinburgh Math. Soc., Vol. 94A, 1-7, 1983.
'A semigroup with an epimorphically embedded subband', Bull. Austral. Math. Soc., Vol. 27, No. 2, 231-242, 1983.
'Saturated and epimorphically closed varieties of semigroups', J. Austral. Math. Soc., Vol. 36, 153-175, 1984.
'Epimorphisms, permutation identities and finite semigroups', Semigroup Forum, Vol. 29, No. 1-2, 87-97, 1984.
'Epimorphisms and semigroup varieties', (Ph. D. summary), Bull. Austral. Math. Soc., Vol. 29, No. 3, 415-417, 1984.
'A new determination of the permutation identities which ensure that a semigroup variety is finitely based', J. Pure and Appl. Algebra, 38, 65-69, 1985.
'Epimorphisms, dominions and semigroups', Algebra Universalis, 21, 225-233, 1985.
'A method of constructing square roots in finite full transformation semigroups', Canad. Math. Bull., Vol. 29 (3), 344-351, 1986.
'Completely semisimple semigroups and epimorphisms', Proc. Amer. Math. Soc., Vol. 96, No. 4, 387-390, 1986.
'Dense subsets of some common classes of semigroup', Semigroup Forum, Vol. 34, 5-19, 1986.
'The naming of popes and a Fibonacci sequence in two non-commuting indeterminates', Fibonacci Quart., Vol. 25, 57-61, February 1987.
'Semigroup classes defined by sequence conditions', Indian J. of Maths. (Ramanujan Centenary Edition), Vol. 29, No. 1, 1-8, 1987.
'Digraphs and the semigroup of all mappings on a finite set', Glasgow Math. J., 30, 41-57, 1988.
'Finite full transformations semigroups as collections of random functions'; (joint with B.M. Brown), Glasgow Math. J., 30, 203-211, 1988.
'The range order of a product of i transformations from a finite full transformation semigroup', Semigroup Forum, Vol. 37, 31-36, 1988.
'Epimorphisms and amalgams', Colloquium Mathematicum, Vol. LVI, No. 1, 1-17, 1988.
'Random functions on a finite set', (joint with E. Williams), Ars Combinatoria, Vol. 26A, 93-102, 1988.
'Embedding in bisimple semigroups', Semigroup Forum, Vol. 40, No. 1, 105-107, 1990.
'An algebraic proof that pseudovarieties are defined by pseudoidentities', Algebra Universalis, 27, 597-99, 1990.
'A short proof of Isbell's zigzag theorem', Pac. J. Math., 144, No. 1, 47-50, 1990.
'Combinatorial results for semigroups of order-preserving mappings', Math. Proc. Camb. Phil. Soc, 113, 281-296, 1993.
'A class of eventually regular semigroups determined by pseudo-random sets', J. London Math. Soc. (2) 48 87-102, 1993.
'The natural partial order of Mitsch', Semigroup Forum, Vol 49, 261-266, 1994.
'Idempotent depth in semigroups of order-preserving mappings', Proc. Roy. Soc. Edin. Vol 124A, 1045-1058, 1994.
'Divisors of the semigroup of order-preserving mappings on a finite chain', International Journal of Algebra and Computation,Vol 5, No. 6 (1995), 725-742.
'Embedding semigroups in semibands of depth two', Semigroup Forum, Vol 51 (1995), 395-96.
'Epis from locally inverse semigroups are onto', Semigroup Forum, Vol 52, (1996) 49-53.
'Ramsey's Theorem in algebraic semigroups', Springer Lecture Note Series, Proc. Tainan - Moscow Algebra Workshop (Walter de Grugter, publishers), (1996) pp 1-36.
'A new proof of Simon's Theorem on piecewise testable languages', Journal of Theoretical Computer Science, 178 257-64, (1997).
'Monoids respecting n-chains of intervals' (joint with J. Almeida) Journal of Algebra, 187, 183-202, (1997).
'Generators and factorizations of transformation semigroups', (joint with J.M. Howie and N. Ruskuc), Proc. Roy. Edin. Math. Soc. 128A , 1355-1369 (1998).
'On relative ranks of full transformation semigroups', (joint with J. Howie and N. Ruskuc), Communications in Algebra, (26)(3), 733-48, (1998).
'The monoid of all orientation-preserving mappings of a cycle', (joint with P. Catarino). Semigroup Forum, 58, (1999) 190-206.
"Finite aperiodic semigroup with commuting idempotents and generalizations", (joint with S.W. Margolis). Israel J. of Mathematics, 116, (2000) 367-380.
"A new proof of Schutzberger's Theorem", International J. of Alg. & Comp., 10, No. 2 (2000), 217-220.
"Remarks concerning Lallements's Lemma and coextentions of eventually regular semigroups", (joint with S.J. Kopamu and P.M. Edwards), Acta Scientarum Mathematicarum, (Szeged) 67 (2001), 385-400.
"The gap between partial and full: an addendum", (joint with J. Almeida and M.V. Volkov), International J. of Alg. & Comp., 11, No. 1 (2001) 131-135..
"Unavoidable Sets of Words of Uniform Length", (joint with C.J. Saker), Computation and Information, 173, 1-5 (2002).
"The pseudovariety generated by the semigroup of all orientation-preserving transformations on a chain", (joint with P. Catarino), International J. of Alg. & Comp., 12, No. 3 (2002), 387-405.
"Set products in transformation semigroups" (joint with J.M. Howie and N. Ruskuc) Proc. Roy. Soc. of Edinburgh, 133A, (2003), 1121-1135.
"Generating the full transformation semigroup using order preserving mappings" (joint with J.D. Mitchell and N. Ruskuc) Glasgow Mathematical Journal, 45, (2003), 557-566.
“Countable versus uncountable ranks in infinite semigroups of transformations and relations”, joint with J.M. Howie, J.D. Mitchell and N. Ruskuc, Proc. Edin. Math. Soc. (2003), 46, 531-544.
“Rank properties of endomorphisms of infinite partially ordered sets”, joint with JD Mitchell, N. Ruskuc and M Morayne Bull. Bulletin of London Math. Soc., 38 (2006), no.2, 177-191.
“The semigroup of conjugates of a word”, International Journal of Algebra and Computation, Vol. 16 No. 6 (2006) 1015-1029.
Unavoidable Sets, Theoretical Computer Science, joint with CJ Saker, Vol. 359, No. 1, (August 2006), 231-238.
Generalized Green's Equivalences on the subsemigroups of the bicyclic monoid, joint with L. Descalco, Communications in Algebra, 38, 4597-4612, (2010).
The map numbering problem, IEEE Transactions, Proceedings CEE'10, 2nd Computer Science and Electronic Engineering Conference, 2010, UK, to appear.
The length of short words in unavoidable sets, International Journal of Algebra and Computation, to appear.
`Techniques of Semigroup Theory', Oxford University Press, Oxford, 1992, (x + 258pp).
'Mathematics for the Curious', Oxford University Press, Oxford & New York 1997
'Mathematics for the Imagination'. Oxford University Press, Oxford & New York, 2002
'The Official Book of 'Cricular Sudoku', Plume Press, 2006.
`Nets, Puzzles and postmen, an exploration of mathematical connections', Oxford University Press 2007.
''Number Story, from counting to cryptography', Springer-Verlag, 2008.
`Numbers, A Very Short Introduction', Oxford University Press, 2011.