4 papers · 1 filter
Balanced Fibonacci word rectangles, and beyond
Jeffrey Shallit, Ingrid Vukusic
Following a recent paper of Anselmo et al., we consider rectangular matrices formed from the Fibonacci word, and we show that their balance properties can be solved wi…
New properties of the -representation of integers
Jeffrey Shallit, Ingrid Vukusic
We prove a few new properties of the -representation of integers, where . In particular, we prove a 2012 conjecture of Kimberling. As software assistants, we…
A Lebesgue variant of the additive square problem
Ingrid Vukusic
The additive square problem is a relatively famous open problem in the area of combinatorics on words: Does there exist an infinite word over a finite alphabet, such that no two co…
On the -adic valuations of values of Legendre polynomials
Max A. Alekseyev, Tewodros Amdeberhan, Jeffrey Shallit +1
We prove an explicit formula for the -adic valuation of the Legendre polynomials evaluated at a prime , and generalize an old conjecture of the third author. We also…