8 papers
State Complexity of Shifts of the Fibonacci Word
Delaram Moradi, Pierre Popoli, Jeffrey Shallit +1
The Fibonacci infinite word is one of the most celebrated objects in combinatorics on words. There is a simple -state automaton tha…
Balanced rectangles over Sturmian words and minimal discrepancy intervals
Ingrid Vukusic
We consider rectangular matrices formed from Sturmian words with slope , and we fully characterise their balance properties in terms of the Ostrowski representations…
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…
More on consecutive multiplicatively dependent triples of integers
Michael A. Bennett, István Pink, Ingrid Vukusic
In this paper, we extend recent work of the third author and Ziegler on triples of integers , with the property that each of , and …
A universal example for quantitative semi-uniform stability
Sahiba Arora, Felix Schwenninger, Ingrid Vukusic +1
We characterise quantitative semi-uniform stability for -semigroups arising from port-Hamiltonian systems, complementing recent works on exponential and strong stability. With…