20 citations · 37 across the 20 of their papers we have counts for
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Euler's partition theorem for all moduli and new companions to Rogers-Ramanujan-Andrews-Gordon identities
XinHua Xiong, William J. Keith
We generalise Euler's partition theorem involving odd parts and different parts for all moduli and provide new companions to Rogers-Ramanujan- Andrews-Gordon identities related to…
A note on nearly platonic graphs
Dalibor Froncek, William J. Keith, Donald L. Kreher
A nearly platonic graph is a k-regular simple planar graph in which all but a small number of the faces have the same degree. We show that it is impossible for a finite graph to ha…
Euler's partition theorem for all moduli and new companions to Rogers-Ramanujan-Andrews-Gordon identities
Xinhua Xiong, William J. Keith
In this paper, we give a conjecture, which generalises Euler's partition theorem involving odd parts and different parts for all moduli. We prove this conjecture for two family par…
The part-frequency matrices of a partition
William J. Keith
A new combinatorial object is introduced, the part-frequency matrix sequence of a partition, which is elementary to describe and is naturally motivated by Glaisher's bijection. We…