20 citations · 271 across the 126 of their papers we have counts for
162 papers
Brown-Gerver-Ramsey Theorems in Small Dimensions
Stijn Cambie, Erik Kalviainen, J. Shallit
We consider infinite walks in with standard unit basis vector steps that avoid collinear points, and show that these walks exist for $(k,t) \in \{(6,3), (4,4), (…
Complexity of Linear Subsequences of -Automatic Sequences
Delaram Moradi, Narad Rampersad, Jeffrey Shallit
We construct automata with input(s) in base recognizing some basic relations and study their number of states. We also consider some basic operations on -automatic sequences…
Repetition Threshold for Binary Automatic Sequences
J. -P. Allouche, N. Rampersad, J. Shallit
The critical exponent of an infinite word is the supremum, over all finite nonempty factors , of the exponent of . In this note we show that for all integers $k\geq 2…
Combinatorics on words and generating Dirichlet series of automatic sequences
Jean-Paul Allouche, Jeffrey Shallit, Manon Stipulanti
Generating series are crucial in enumerative combinatorics, analytic combinatorics, and combinatorics on words. Though it might seem at first view that generating Dirichlet series…
A General Approach to Proving Properties of Fibonacci Representations via Automata Theory
Jeffrey Shallit, Sonja Linghui Shan
We provide a method, based on automata theory, to mechanically prove the correctness of many numeration systems based on Fibonacci numbers. With it, long case-based and induction-b…
Proving properties of some greedily-defined integer recurrences via automata theory
Jeffrey Shallit
Venkatachala on the one hand, and Avdispahić & Zejnulahi on the other, both studiied integer sequences with an unusual sum property defined in a greedy way, and proved many results…