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Arithmetic Properties of Non-Squashing Partitions into Distinct Parts
Øystein J. Rodseth1, James A. Sellers2 and Kevin M. Courtright2
1Department of Mathematics, University of Bergen, Johs. Brunsgt. 12, 5008 Bergen, Norway
2Department of Mathematics, Penn State University, University Park, PA 16802, USA
sellersj@math.psu.edu, kmc260@psu.edu
Annals of Combinatorics 8 (3) p.347-353 September, 2004
AMS Subject Classification:05A17, 11P83
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 2r-2 is the exact power of 2 dividing the difference for n odd and r2.

Keywords: partitions, non-squashing partitions, stacking boxes, congruences


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.