Arithmetic Properties of Non-Squashing
Partitions into Distinct Parts

Øystein J. Rodseth^{1}, James A. Sellers^{2} and Kevin M. Courtright^{2}

rodseth@mi.uib.no

sellersj@math.psu.edu, kmc260@psu.edu

Annals of Combinatorics 8 (3) p.347-353 September, 2004

Abstract:

A partition
with is non-squashing if .
On their way towards the solution of a certain box-stacking problem, Sloane
and Sellers were led to consider the number *b*(*n*) of non-squashing
partitions of *n* into distinct parts. Sloane and Sellers did briefly consider
congruences for *b*(*n*) modulo 2. In this paper we show that 2^{r-2}
is the exact power of 2 dividing the difference
for *n* odd and *r*2.

References:

1. M.D. Hirschhorn and J.A. Sellers, A different view of *m*-ary partitions, Australas. J. Combin.
30 (2004) 193--196.

2. Ø.J. Røseth and J.A. Sellers, Binary partitions revisited, J. Combin. Theory, Ser. A 98 (2002) 33--45.

3. N.J.A. Sloane, The On-Line Encyclopedia of Integer Sequences, 2003, published electronically at http://www.research.att.com/~njas/sequences/.

4. N.J.A. Sloane and J.A. Sellers, On non-squashing partitions, to appear, http://arxiv.org/abs/math.CO/0312418.