15 citations · 105 across the 67 of their papers we have counts for
15 papers · 1 filter
Abelian Complexity and Synchronization
Jeffrey Shallit
We present a general method for computing the abelian complexity of an automatic sequence in the case where (a) is bounded…
Subword complexity of the Fibonacci-Thue-Morse sequence: the proof of Dekking's conjecture
Jeffrey Shallit
Recently Dekking conjectured the form of the subword complexity function for the Fibonacci-Thue-Morse sequence. In this note we prove his conjecture by purely computational means,…
The Largest Entry in the Inverse of a Vandermonde Matrix
Carlo Sanna, Jeffrey Shallit, Shun Zhang
We investigate the size of the largest entry (in absolute value) in the inverse of certain Vandermonde matrices. More precisely, for every real , let be the maximum…
Robbins and Ardila meet Berstel
Jeffrey Shallit
In 1996, Neville Robbins proved the amazing fact that the coefficient of in the Fibonacci infinite product $$ \prod_{n \geq 2} (1-X^{F_n}) = (1-X)(1-X^2)(1-X^3)(1-X^5)(1-X^8)…
The Simplest Binary Word with Only Three Squares
Daniel Gabric, Jeffrey Shallit
We re-examine previous constructions of infinite binary words containing few distinct squares with the goal of finding the "simplest", in a certain sense. We exhibit several new co…
Badly approximable numbers, Kronecker's theorem, and diversity of Sturmian characteristic sequences
Dmitry Badziahin, Jeffrey Shallit
We give an optimal version of the classical ``three-gap theorem'' on the fractional parts of , in the case where is an irrational number that is badly approximable. As a c…