5 papers
The speed of convergence in greedy Galois games
Jeffrey Shallit
In 2013 Cooper and Dutle invented a dueling scenario where Alice and Bob shoot at each other until one is hit. Each shot is successful with some fixed probability , .…
Beatty Sequences for a Quadratic Irrational: Decidability and Applications
Luke Schaeffer, Jeffrey Shallit, Stefan Zorcic
Let and belong to the same quadratic field. We show that the inhomogeneous Beatty sequence is synchronized, in the sense that there…
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…
The reflection complexity of sequences over finite alphabets
Jean-Paul Allouche, John M. Campbell, Shuo Li +2
In combinatorics on words, the well-studied factor complexity function $Ï_{\infw{x}}$ of a sequence $\infw{x}$ over a finite alphabet counts, for every nonnegative integer , th…
Effective Computation of Generalized Abelian Complexity for Pisot Type Substitutive Sequences
Jean-Michel Couvreur, Martin Delacourt, Nicolas Ollinger +3
Generalized abelian equivalence compares words by their factors up to a certain bounded length. The associated complexity function counts the equivalence classes for factors of a g…