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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
rodseth@mi.uib.no
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
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 2r-2 is the exact power of 2 dividing the difference for n odd and r2.

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

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.