5 papers
Dense signed sums of non-integer powers
David Treeby
We prove that if is not an integer, then there is a choice of signs such that the partial sums are dense in $\m…
Straight-line optimality in Bellman's lost-in-a-forest problem for Euclidean balls
David Treeby, Edward Wang
We prove that among all unit-speed paths, a straight line minimises the expected escape time from a ball in , solving the min-mean variant of Bellman's Lost~in~a~Fore…
Structure and Growth of Galileo Sequences
William Cheah, David Treeby
A Galileo sequence \((a_n)\) is a sequence of positive integers whose partial sums satisfy for some . In this paper we prove that every polynomial Galileo…
Pick-up Sticks and the Fibonacci Factorial
Aidan Sudbury, Arthur Sun, David Treeby +1
We present a variation of the broken stick problem in which stick lengths are sampled uniformly at random. We prove that the probability that no three sticks can form a triangl…
An Extension of the Prouhet-Tarry-Escott Problem to Nonnegative, Noninteger Powers
David Treeby, Edward Wang
We present an extension of the Prouhet-Tarry-Escott problem by demonstrating that signed sums of noninteger powers of consecutive integers can be made arbitrarily close to zero.