R. Arthur Knoebel’s research while affiliated with New Mexico State University and other places

... This question comes as a natural probabilistic extension of the long history of study of power towers, which we outline briefly below. Power towers have usually been studied as a topic of inherent interest, but they do occasionally find applications in other topics (see for example [5], [9], or [12]). They also provide a simple example of a non-trivial discrete dynamical system. ...

Reference:

Infinite random power towers

... A most remarkable result concerning iterated exponentials, first discovered by L. Euler in 1777 and subsequently re-discovered and proven in several papers, is shown below. 7 Here, its statement is taken with slight changes from [17]. ...

Reference:

On generalised Ackermann encodings -- the basis issue