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On m-Ary Overpartitions
Østein J. Røseth1 and James A. Sellers2
1Department of Mathematics, University of Bergen, Johs. Brunsgt. 12, N–5008 Bergen, Norway
rodseth@mi.uib.no
2Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA
sellersj@math.psu.edu
Annals of Combinatorics 9 (3) p.345-353 September, 2005
AMS Subject Classification: 05A17, 11P83
Abstract:
Presently there is a lot of activity in the study of overpartitions, objects that were discussed by MacMahon, and which have recently proven useful in several combinatorial studies of basic hypergeometric series. In this paper we study some similar objects, which we name m-ary overpartitions. We consider divisibility properties of the number of m-ary overpartitions of a natural number, and we prove a theorem which is a lifting to general m of the well-known Churchhouse congruences for the binary partition function.
Keywords: overpartition, m-ary overpartition, generating function, partition

References:

1. R.F. Churchhouse, Congruence properties of the binary partition function, Proc. Cambridge Philos. Soc. 66 (1969) 371--376.

2. S. Corteel and J. Lovejoy, Overpartitions, Trans. Amer. Math. Soc. 356 (2004) 1623--1635.

3. Ø. J. Røseth and J.A. Sellers, On m-ary partition function congruences: A fresh look at a past problem, J. Number Theory 87 (2001) 270--281.

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