On certain restricted integer partitions - Rapudi, Molatelo Olgar (My University, 2019)
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
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