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A note on Andrews-MacMahon theorem
Darlison Nyirenda
For a positive integer , George Andrews proved that the set of partitions of in which odd multiplicities are at least is equinumerous with the set of partitions of…
Modulo 2 congruences for partitions with initial repetitions
Darlison Nyirenda, Beaullah Mugwangwavari
Motivated by Andrews' partitions with initial repetitions, we derive parity formulas for several functions for this class of partitions. In many cases, we present an infinite famil…
Legendre theorems for a class of partitions with initial repetitions
Darlison Nyirenda, Beaullah Mugwangwavari
Partitions with initial repetitions were introduced by George Andrews. We consider a subclass of these partitions and find Legendre theorems associated with their respective partit…
Some consequences of Glaisher's map and a generalization of Sylvester's theorem
Darlison Nyirenda, Molatelo Rapudi
For positive integers , the set of -regular partitions in which parts appear at most times has attracted a lot of interest in that a composition of Glaisher's m…
Extensions and variations of Andrews-Merca identities
Darlison Nyirenda, Beaullah Mugwangwavari
Recently, Andrews and Merca have given a new combinatorial interpretation of the total number of even parts in all partitions of n into distinct parts. We generalise this result an…
On generalizations of theorems of MacMahon and Subbarao
Darlison Nyirenda, Beaullah Mugwangwavari
In this paper, we consider various theorems of P.A. MacMahon and M.V. Subbarao. For a non-negative integer , MacMahon proved that the number of partitions of wherein parts h…