1 citations · 1 across the 13 of their papers we have counts for
14 papers
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…
Power Partitions and Semi-m-Fibonacci Partitions
Abdulaziz M. Alanazi, Augustine O. Munagi, Darlison Nyirenda
George Andrews recently proved a new identity between the cardinalities of the set of Semi-Fibonacci partitions and the set of partitions into powers of two with all parts appearin…
A simplification and generalization of Elsayed's two-dimensional system of third order difference equations
M. Folly-Gbetoula, D. Nyirenda
A full Lie analysis of a system of third-order difference equations is performed. Explicit solutions, expressed in terms of the initial values, are derived. Furthermore, we give su…
On a system of second-order difference equations
M Folly-Gbetoula, D. Nyirenda
We obtain explicit formulas for the solutions of the system of second-order difference equations of the form $x_{n+ 1} = \frac{x_n y_{n-1}}{y_n (a_n + b_n x_n y_{n - 1})}, \quad y_…
On certain rational recursive sequences of order four
Mensah Folly-Gbetoula, Darlison Nyirenda
We obtain solutions to the recursive sequences of the form where and are arbitrary sequences o…
On certain sixth order difference equations
D. Nyirenda, M. Folly-Gbetoula
We use the Lie group analysis method to investigate the invariance properties and the solutions of \begin{align*} x_{n+1} =\frac{x_{n-5}x_{n-3}}{x_{n-1}(a_n +b_nx_{n-5}x_{n-3})}. \…
The invariance and formulas for solutions of some fifth-order difference equations
D. Nyirenda, M. Folly-Gbetoula
Lie group analysis of the difference equations of the form \begin{align*} x_{n+1} =\frac{x_{n-4}x_{n-3}}{x_{n}(a_n +b_nx_{n-4}x_{n-3}x_{n-2}x_{n-1})}, \end{align*} where and…
On Andrews' partitions with parts separated by parity
Abdulaziz M. Alanazi, Darlison Nyirenda
In this paper, we present a generalization of one of the theorems in [G. E. Andrews, Partitions with parts separated by parity, \textit{Annals of Combinatorics} \textbf{23}(2019),…
Generalising a finite version of Euler's partition identity
Darlison Nyirenda
Recently, George Andrews has given a Glaisher style proof of a finite version of Euler's partition identity. We generalise this result by giving a finite version of Glaisher's part…