Please note: This master’s thesis presentation will be given online.
Trevor
Clokie, Master’s
candidate
David
R.
Cheriton
School
of
Computer
Science
Supervisor: Professor Jeffrey Shallit
Let s_2(n) be the sum of the digits of n when expressed in base 2. For integers n and k, Stolarsky defined n to be k-flimsy if s_2(kn) < s_2(n). In this paper, we generalize the definition of k-flimsy numbers to all bases b, and provide a method to construct a pushdown automaton recognizing the k-flimsy base-b numbers. Using the tools of context-free languages and analytic combinatorics, we use this automaton to determine precise asymptotics for the number of k-flimsy N-digit numbers in base b. Lastly, using the results we obtained, we discuss the natural densities of k-flimsy numbers in base b for all values k and b.
Our main results can be found in Theorems 2, 3, 8, and 9.
To joint this master’s thesis presentation on Zoom, please go to https://us02web.zoom.us/j/88171362356?pwd=L2hNN3hUN3BGMTdoYUI4ZlVNNTdsQT09.