4 papers
Scaled Arndt Compositions
Brian Hopkins, Augustine Munagi
Integer compositions restricted by inequalities on certain pairs of parts were first considered by Jörg Arndt in 2013 and several variations have been studied recently. Here we co…
Signed Partitions and Rogers-Ramanujan type Identities
Abdulaziz M. Alanazi, Augustine O. Munagi, Andrew V. Sills
George Andrews [\emph{Bull. Amer. Math. Soc.}, 2007, 561--573] introduced the idea of a \emph{signed partiton} of an integer; similar to an ordinary integer partitions, but where s…
"Overpartitionized" Rogers--Ramanujan type identities
Abdulaziz Alanazi, Augustine O. Munagi, Andrew V. Sills
Many classical -series identities, such as the Rogers--Ramanujan identities, yield combinatorial interpretations in terms of integer partitions. Here we consider algebraically m…
Some Properties of Overpartitions into Nonmultiples of Two Integers
Abdulaziz M. Alanazi, Augustine O. Munagi, Manjil P. Saikia
We consider properties of overpartitions that are simultaneously {\ell}-regular and μ-regular, where {\ell} and μ are positive relatively prime integers. We prove a seven-way com…