We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
$m$-FIBONACCI PARTITIONS
Andrews [‘Binary and semi-Fibonacci partitions’, J. Ramanujan Soc. Math. Math. Sci.7(1) (2019), 1–6] recently proved a new identity between the cardinalities of the set of semi-Fibonacci partitions and the set of partitions into powers of 2 with all parts appearing an odd number of times. We extend the identity to the set of semi-
$m$-Fibonacci partitions of 
$n$ and the set of partitions of 
$n$ into powers of 
$m$ in which all parts appear with multiplicity not divisible by 
$m$. We also give a new characterisation of semi-
$m$-Fibonacci partitions and some congruences satisfied by the associated number sequence.
