On certain restricted integer partitions
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Date
2019
Authors
Rapudi, Molatelo Olgar
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Abstract
In this dissertation, we study some restricted integer partition functions. We first give a survey of some aspects of integer partition theory that will form a foundation of our work. These include but are not limited to, the Jacobi’s triple product identity and its consequences, known recurrences such as MacMahon’s recurrence for the partition function and Frobenius partitions. Our contributions to partition theory is a generalisation of one of the theorems of Sylvester, a non-trivial extension of a version of Alladi-Schur’s theorem and a derivation of several parity and recurrence formulas of Sylvester-related partition functions and Frobenius partitions
Description
A Dissertation Presented
to
The Faculty of Science, University of the Witwatersrand,
Johannesburg
in fulfillment of the requirements
for the degree of Master of Science
in Mathematics
April, 2019