The Calkin-Wilf tree is well-known as one way to enumerate the rationals, but also may be used to count hyperbinary partitions of an integer, h2(n). We present an m-ary tree which is a generalization of the Calkin-Wilf tree and show how it may be used to count the hyper m-ary partitions of an integer, hm(n). We then use properties of the m-ary tree to prove an identity relating values of h2 to values of hm, showing that one sequence is a subsequence of the other. Finally, we give a bijection between the partitions to reprove our identity.
Flower, T.B. & Lockard, S.R. (2016). Identifying an m-Ary Partition Identity through an m-Ary Tree. Integers, 16, #A10, 1-10.
Virtual Commons Citation
Flower, Timothy B. and Lockard, Shannon R. (2016). Identifying an m-Ary Partition Identity through an m-Ary Tree. In Mathematics Faculty Publications. Paper 63.
Available at: https://vc.bridgew.edu/math_fac/63