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On a Restricted m-Non-Squashing Partition Function
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Øystein J. Rødseth

Department of Mathematics

University of Bergen

Johs. Brunsgt. 12

N-5008 Bergen

NORWAY

James A. Sellers

Department of Mathematics

Penn State University

University Park, PA 16802

USA

**Abstract:**

For a fixed integer , we say that a partition
of a natural number is -non-squashing
if and
for
. In this paper we give a new bijective proof that the
number of -non-squashing partitions of is equal to the number
of -ary partitions of . Moreover, we prove a similar result
for a certain restricted -non-squashing partition function
which is a natural generalization of the function which
enumerates non-squashing partitions into distinct parts (originally
introduced by Sloane and the second author). Finally, we prove that
for each integer ,

where
.

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(Concerned with sequences
A000123
A005704
A005705
A005706
A018819
A088567 and
A090678
.)

Received April 20 2005;
revised version received October 23 2005.
Published in *Journal of Integer Sequences* October 24 2005.

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