Explanipedia

A NEW REFINEMENT OF FINE’S PARTITION THEOREM Open

Jiayu Kang, Runqiao Li, Andrew Y. Z. Wang · 2021

We find a new refinement of Fine’s partition theorem on partitions into distinct parts with the minimum part odd. As a consequence, we obtain two companion partition identities. Both analytic and combinatorial proofs are provided.

INFINITE FAMILIES OF CONGRUENCES FOR OVERPARTITIONS WITH RESTRICTED ODD DIFFERENCES Open

Bernard L. S. Lin, Jian Liu, Andrew Y. Z. Wang, Jiejuan Xiao · 2020

Let $\overline{t}(n)$ be the number of overpartitions in which (i) the difference between successive parts may be odd only if the larger part is overlined and (ii) if the smallest part is odd then it is overlined. Ramanujan-type congruence…

GENERALISATION OF A RESULT ON DISTINCT PARTITIONS WITH BOUNDED PART DIFFERENCES Open

Runqiao Li, Bernard L. S. Lin, Andrew Y. Z. Wang · 2019

We generalise a result of Chern [‘A curious identity and its applications to partitions with bounded part differences’, New Zealand J. Math. 47 (2017), 23–26] on distinct partitions with bounded difference between largest and smallest part…

Powerful Sets: a Generalisation of Binary Matroids Open

Graham Farr, Andrew Y. Z. Wang · 2018

A set $S\subseteq\{0,1\}^E$ of binary vectors, with positions indexed by $E$, is said to be a powerful code if, for all $X\subseteq E$, the number of vectors in $S$ that are zero in the positions indexed by $X$ is a power of 2. By treating…

Arithmetic Properties of a Restricted Bipartition Function Open

Jian Liu, Andrew Y. Z. Wang · 2015

A bipartition of $n$ is an ordered pair of partitions $(\lambda,\mu)$ such that the sum of all of the parts equals $n$. In this article, we concentrate on the function $c_5(n)$, which counts the number of bipartitions $(\lambda,\mu)$ of $n…

On the partial finite sums of the reciprocals of the Fibonacci numbers Open

Andrew Y. Z. Wang, Peibo Wen · 2015

In this article, we obtain two interesting families of partial finite sums of the reciprocals of the Fibonacci numbers, which substantially improve two recent results involving the reciprocal Fibonacci numbers. In addition, we present an a…

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