A positive linear fractional transformation (PLFT) is a function of the form f (z) = az+b cz+d where a, b, c and d are nonnegative integers with determinant ad − bc = 0. Nathanson generalized the notion of the Calkin-Wilf tree to PLFTs and used it to partition the set of PLFTs into an infinite forest of rooted trees. The roots of these PLFT Calkin-Wilf… (More)
We study the behavior of Conway's RATS (reverse-add-then-sort) sequences in base 3. An independent proof is given of Gentges' result that all RATS sequences in base 3 are ultimately periodic. We also prove Erd˝ os-Kac and Hardy-Ramanujan type results for the periods of such sequences.
In this article, we examine the existence of nice arrangements of stars on the Ameri-can flag. We show that despite the existence of such arrangements for any number of stars from 1 to 100, with the exception of 29, 69 and 87, they are rare as the number of stars increases. 1. INTRODUCTION. The Union Jack is the blue, upper left portion of the American flag… (More)