#### Publication Date

2016

#### Document Type

Article

#### Abstract

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, *h*_{2}(*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, *h*_{m}(*n*). We then use properties of the *m*-ary tree to prove an identity relating values of *h*_{2} to values of *h _{m}*, showing that one sequence is a subsequence of the other. Finally, we give a bijection between the partitions to reprove our identity.

#### Original Citation

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: http://vc.bridgew.edu/math_fac/63