Jeffrey Shallit

collaborators

3 papers

cs.FL2025

The Tribonacci constant and finite automata

Jeffrey Shallit

We show that there is no automaton accepting the Tribonacci representations of $n$ and $x$ in parallel, where $ψ = 1.839 \dots$ is the Tribonacci constant, and $x= \lfloor n ψ\rfloo…

math.NT2025

On the $p$ -adic valuations of values of Legendre polynomials

Max A. Alekseyev, Tewodros Amdeberhan, Jeffrey Shallit +1

We prove an explicit formula for the $p$ -adic valuation of the Legendre polynomials $P_{n} (x)$ evaluated at a prime $p$ , and generalize an old conjecture of the third author. We also…

math.CO2024

Christoffel Matrices and Sturmian Determinants

Christophe Reutenauer, Jeffrey Shallit

We discuss certain matrices associated with Christoffel words, and show that they have a group structure. We compute their determinants and show a relationship between the Zolotare…

The Tribonacci constant and finite automata

On the p-adic valuations of values of Legendre polynomials

Christoffel Matrices and Sturmian Determinants

On the $p$ -adic valuations of values of Legendre polynomials