I have a PhD, in combinatorial number theory, from The University of Sussex http://sro.sussex.ac.uk/view/creators/5315.default.html I now teach maths, physics, and engineering at the University of Brighton International College https://www.kaplanpathways.com/colleges/university-of-brighton-international-college/ Supervisors: My doctoral supervisor was Dr Richard Lewis Address: The University of Brighton International College, University of Brighton
This thesis is concerned mainly with the interplay between identities involving power series (whi... more This thesis is concerned mainly with the interplay between identities involving power series (which are called q-series) and combinatorics, in particular the theory of partitions. The thesis includes new proofs of some q-series identities and some ideas about the generating functions for the rank and crank, a new proof of the triple product identity and a combinatorial proof of a q-elliptic identity.
International Journal of Mathematics and …, Jan 1, 2004
Dyson defined the rank of a partition (as the first part minus the number of parts) whilst invest... more Dyson defined the rank of a partition (as the first part minus the number of parts) whilst investigating certain congruences in the sequence p−1(n). The rank has been widely studied as have been other statistics, such as the crank. In this paper a birank is defined which relates to ordered pairs of partitions, and is used in an elementary proof of a congruence in p−2(n).
Bulletin of the Australian Mathematical Society, 1999
We prove a general identity between power series and use this identity to give proofs of a number... more We prove a general identity between power series and use this identity to give proofs of a number of identities proposed by M.D. Hirschhorn. We also use the identity to give proofs of a well-known result of Jacobi, the quintuple-product identity and Winquist's identity.
This thesis is concerned mainly with the interplay between identities involving power series (whi... more This thesis is concerned mainly with the interplay between identities involving power series (which are called q-series) and combinatorics, in particular the theory of partitions. The thesis includes new proofs of some q-series identities and some ideas about the generating functions for the rank and crank, a new proof of the triple product identity and a combinatorial proof of a q-elliptic identity.
International Journal of Mathematics and …, Jan 1, 2004
Dyson defined the rank of a partition (as the first part minus the number of parts) whilst invest... more Dyson defined the rank of a partition (as the first part minus the number of parts) whilst investigating certain congruences in the sequence p−1(n). The rank has been widely studied as have been other statistics, such as the crank. In this paper a birank is defined which relates to ordered pairs of partitions, and is used in an elementary proof of a congruence in p−2(n).
Bulletin of the Australian Mathematical Society, 1999
We prove a general identity between power series and use this identity to give proofs of a number... more We prove a general identity between power series and use this identity to give proofs of a number of identities proposed by M.D. Hirschhorn. We also use the identity to give proofs of a well-known result of Jacobi, the quintuple-product identity and Winquist's identity.
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Papers by Paul Hammond