POWER PARTITIONS AND SEMI-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.