On m-ary overpartitions

被引：8
|
作者：
Rodseth, Oystein J.
Sellers, James A.
机构：
[1] Univ Bergen, Dept Math, N-5008 Bergen, Norway
[2] Penn State Univ, Dept Math, University Pk, PA 16802 USA
来源：
ANNALS OF COMBINATORICS | 2005年 / 9卷 / 03期
关键词：
overpartition; m-ary overpartition; generating function; partition;
D O I：
10.1007/s00026-005-0262-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Presently there are a lot of activities 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.
引用
收藏
页码：345 / 353
页数：9
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