If M is a monoid, and A is an abelian group, then A is a compact abelian group; a linear cellular automaton (LCA) is a continuous endomorphism F : Aâˆ’â†’A that commutes with all shift maps. If F isâ€¦ (More)

In this paper we use the framework of automatic sequences to study combinatorial sequences modulo prime powers. Given a sequence whose generating function is the diagonal of a rational power series,â€¦ (More)

Let M = Z be a D-dimensional lattice, and let (A,+) be an abelian group. AM is then a compact abelian group under componentwise addition. A continuous function : AM âˆ’â†’ AM is called a linear cellularâ€¦ (More)

Let M be a monoid (e.g. N, Z, or Z), and A an abelian group. A is then a compact abelian group; a linear cellular automaton (LCA) is a continuous endomorphism F : A âˆ’â†’ A that commutes with all shiftâ€¦ (More)

We show that a sequence over a finite field Fq of characteristic p is p-automatic if and only if it occurs as a column of the spacetime diagram, with eventually periodic initial conditions, of aâ€¦ (More)

We investigate different notions of recognizability for a free monoid morphism Ïƒ : Aâˆ— â†’ Bâˆ—. Full recognizability occurs when each (aperiodic) point in BZ admits at most one tiling with words Ïƒ(a), aâ€¦ (More)

Many dynamical systems can be naturally represented as Bratteli-Vershik (or adic) systems, which provide an appealing combinatorial description of their dynamics. If an adic system X satisfies twoâ€¦ (More)

Recent work has shown that many cellular automata (CA) have configurations whose orbit closures are isomorphic to odometers. We investigate the geometry of the spacetime diagrams of these â€˜odometerâ€¦ (More)

If L = ZD is a D-dimensional lattice, and A is a finite set, then A is a compact space; a cellular automaton (CA) is a continuous transformation Î¦ : Aâˆ’â†’A that commutes with all shift maps. If Î¼ is aâ€¦ (More)

If M is a monoid, and A is an abelian group, then A is a compact abelian group; a linear cellular automaton (LCA) is a continuous endomorphism F : A âˆ’â†’ A that commutes with all shift maps. If F isâ€¦ (More)