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math.CO2022
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…
math.CO2022
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…
math.CO2022★ 1 cited
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…