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POWER PARTITIONS AND SEMI-
$m$-FIBONACCI PARTITIONS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 102 / Issue 3 / December 2020
- Published online by Cambridge University Press:
- 20 February 2020, pp. 418-429
- Print publication:
- December 2020
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- Article
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- You have access
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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.
