[seqfan] Partitions into non-integral powers
franktaw at netscape.net
franktaw at netscape.net
Fri Jul 3 05:20:43 CEST 2009
There are 12 sequences (A000135, A000148, A000158, A000160, A000263,
A000298, A000327, A000333, A000339, A000345, A000347, and A000397) with
the title "Number of partitions into non-integral powers". A000234,
with title "Partitions into non-integral powers (see Comments for
precise definition)." has an explanation (thanks to Richard Mather);
none of these others do.
All these sequences reference a paper: "B. K. Agarwala and F. C.
Auluck, Statistical mechanics and partitions into non-integral powers
of integers, Proc. Camb. Phil. Soc., 47 (1951), 207-216.". Sequence
A000093, "[ n^(3/2) ]" (which should really be "floor(n^(3/2))" also
references this paper, although there is no obvious connection.
It would be nice if somebody could look at this paper and provide
explanations for the remaining sequences.
Franklin T. Adams-Watters
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