Two congruences involving Andrews-Paule’s broken 3-diamond partitions and 5-diamond partitions
نویسندگان
چکیده
منابع مشابه
An extensive analysis of the parity of broken 3-diamond partitions.
In 2007, Andrews and Paule introduced the family of functions [Formula: see text] which enumerate the number of broken k-diamond partitions for a fixed positive integer k. Since then, numerous mathematicians have considered partitions congruences satisfied by [Formula: see text] for small values of k. In this work, we provide an extensive analysis of the parity of the function [Formula: see tex...
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Abstract. In 2007, Andrews and Paule introduced the family of functions ∆k(n) which enumerate the number of broken k–diamond partitions for a fixed positive integer k. In that paper, Andrews and Paule proved that, for all n ≥ 0, ∆1(2n + 1) ≡ 0 (mod 3) using a standard generating function argument. Soon after, Shishuo Fu provided a combinatorial proof of this same congruence. Fu also utilized th...
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 2011
ISSN: 0386-2194
DOI: 10.3792/pjaa.87.65