3 citations · 5 across the 4 of their papers we have counts for
4 papers
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…
Automatic Sequences in Negative Bases and Proofs of Some Conjectures of Shevelev
Jeffrey Shallit, Sonja Linghui Shan, Kai Hsiang Yang
We discuss the use of negative bases in automatic sequences. Recently the theorem-prover Walnut has been extended to allow the use of base (-k) to express variables, thus permittin…
Pseudoperiodic Words and a Question of Shevelev
Joseph Meleshko, Pascal Ochem, Jeffrey Shallit +1
We generalize the familiar notion of periodicity in sequences to a new kind of pseudoperiodicity, and we prove some basic results about it. We revisit the results of a 2012 paper o…
On the existence and non-existence of improper homomorphisms of oriented and -edge-coloured graphs to reflexive targets
Christopher Duffy, Sonja Linghui Shan
We consider non-trivial homomorphisms to reflexive oriented graphs in which some pair of adjacent vertices have the same image. Using a notion of convexity for oriented graphs, we…