Jeffrey Shallit

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20242026

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math.CO2026

An infinite walk in $N^{16}$ , using only unit steps, with no three collinear points

Jeffrey Shallit

Is it possible to walk to infinity, avoiding three collinear points, using as steps only the standard unit basis vectors $(0, 0, \dots, 0, 1, 0, \dots, 0)$ ? We prove this is possib…

math.CO2025

On a sequence of Kimberling and its relationship to the Tribonacci word

Lubomíra Dvořáková, Edita Pelantová, Jeffrey Shallit

In 2017, Clark Kimberling defined an interesting sequence $B = 0100101100 \dots$ of $0$ 's and $1$ 's by certain inflation rules, and he made a number of conjectures about thi…

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…

An infinite walk in N16, using only unit steps, with no three collinear points

On a sequence of Kimberling and its relationship to the Tribonacci word

Christoffel Matrices and Sturmian Determinants

An infinite walk in $N^{16}$ , using only unit steps, with no three collinear points