no code implementations • 16 Feb 2021 • Philipp Hieronymi, Dun Ma, Reed Oei, Luke Schaeffer, Christian Schulz, Jeffrey Shallit
We show that the first-order theory of Sturmian words over Presburger arithmetic is decidable.
Logic in Computer Science Combinatorics Logic
no code implementations • 12 Dec 2020 • Jeffrey Shallit
We also prove analogous results for other sequences, including the Thue-Morse sequence and the Tribonacci sequence.
Formal Languages and Automata Theory Discrete Mathematics Combinatorics
no code implementations • 29 Jul 2020 • Jeffrey Shallit
In 1996, Neville Robbins proved the amazing fact that the coefficient of $X^n$ in the Fibonacci infinite product $$ \prod_{n \geq 2} (1-X^{F_n}) = (1-X)(1-X^2)(1-X^3)(1-X^5)(1-X^8) \cdots = 1-X-X^2+X^4 + \cdots$$ is always either $-1$, $0$, or $1$.
Combinatorics Discrete Mathematics Formal Languages and Automata Theory Number Theory
no code implementations • 30 Jun 2017 • Aayush Rajasekaran, Jeffrey Shallit, Tim Smith
We prove, using a decision procedure based on automata, that every natural number is the sum of at most 4 natural numbers whose base-2 representation is a palindrome.
Formal Languages and Automata Theory Combinatorics Number Theory
