Minimal r-Complete Partitions
Øystein J. Rödseth
Department of Mathematics
University of Bergen
Johs. Brunsgt. 12
A minimal r-complete partition of an integer m is a partition of
m with as few parts as possible, such that all the numbers
1,..., rm can be written as a sum of parts taken from the
partition, each part being used at most r times. This is a
generalization of M-partitions (minimal 1-complete partitions). The
number of M-partitions of m was recently connected to the binary
partition function and two related arithmetic functions. In this
paper we study the case r ≥ 2, and connect the number of minimal
r-complete partitions to the (r+1)-ary partition function and a
related arithmetic function.
Full version: pdf,
(Concerned with sequences
Received May 14 2007;
revised version received July 30 2007.
Published in Journal of Integer Sequences, August 3 2007.
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