Alonso Castillo-Ramirez

activity

20132026

most citedCellular Automata and Finite Groups

12 citations · 82 across the 30 of their papers we have counts for

collaborators

33 papers

cond-mat.mes-hall2026

Coherent and dissipative coupling of multiple photon-magnon hybrids in a chiral microwave resonator

Supanat Chantarattana, Charlie W. F. Freeman, Daniel Prestwood +3

We demonstrate control between level repulsion and level attraction of photon-magnon coupling spectra in a chiral microwave-photon resonator loaded with a 2 mm YIG sphere. By syste…

math.GR2026

When do lazy and invertible cellular automata generate all cellular automata?

Edgar Alcalá-Arroyo, Alonso Castillo-Ramirez

Let $G$ be a group and let $A$ be a set with at least two elements. A lazy cellular automaton over $A^{G}$ acts as the identity except at the cells where a fixed pattern occurs, wher…

math.GR2026

A characterization of the reversibility of linear cellular automata

Alonso Castillo-Ramirez

Let $G$ be a group, let $K$ be a field, and let $V$ be a $K$ -vector space. We prove that there exists a bijective linear cellular automaton $V^{G} \to V^{G}$ whose inv…

math.RA2026

Fusion rules from the Norton inequality

Alonso Castillo-Ramirez

The Norton inequality is one of the fundamental axioms in the theory of Majorana and axial algebras, yet its precise structural consequences have remained only partially understood…

math.DS2026

Topological Dynamics of Pullback Maps on Full Shifts

Alonso Castillo-Ramirez, Luguis De Los Santos Baños

Let $G$ be a group, let $A$ be a finite alphabet, and let $ϕ : G \to G$ be an endomorphism. We study the topological dynamics of the pullback map $ϕ^{*} : A^{G} \to A^{G}$ , given by $ϕ^*(…

cs.FL2026

A categorical framework for cellular automata

A. Castillo-Ramirez, A. Vazquez-Aceves, A. Zaldivar-Corichi

This paper proposes a generalized framework for cellular automata using the language of category theory, extending the classical definition beyond set-theoretic constraints. For an…

cs.FL2025

On the order of lazy cellular automata

Edgar Alcalá-Arroyo, Alonso Castillo-Ramirez

We study the most elementary family of cellular automata defined over an arbitrary group universe $G$ and an alphabet $A$ : the lazy cellular automata, which act as the identity on…

nlin.CG2025

Categorical products of cellular automata

Alonso Castillo-Ramirez, Alejandro Vazquez-Aceves, Angel Zaldivar-Corichi

We study two categories of cellular automata. First, for any group $G$ , we consider the category $C A (G)$ whose objects are configuration spaces of the form $A^{G}$ , where $…

nlin.CG2025

Connections between the minimal neighborhood and the activity value of cellular automata

Alonso Castillo-Ramirez, Eduardo Veliz-Quintero

For a group $G$ and a finite set $A$ , a cellular automaton is a transformation of the configuration space $A^{G}$ defined via a finite neighborhood and a local map. Although neighbor…

nlin.CG2024

One-dimensional cellular automata with a unique active transition

Alonso Castillo-Ramirez, Maria G. Magaña-Chavez, Luguis de los Santos Baños

A one-dimensional cellular automaton $τ : A^{Z} \to A^{Z}$ is a transformation of the full shift defined via a finite neighborhood $S \subset Z$ and a local f…

nlin.CG2024★ 1 cited

On the minimal memory set of cellular automata

Alonso Castillo-Ramirez, Eduardo Veliz-Quintero

For a group $G$ and a finite set $A$ , a cellular automaton (CA) is a transformation $τ : A^{G} \to A^{G}$ defined via a finite memory set $S \subseteq G$ and a local map $μ : A^{S} \to A$ .…

math.GR2024★ 4 cited

Idempotent cellular automata and their natural order

Alonso Castillo-Ramirez, Maria G. Magaña-Chavez, Eduardo Veliz-Quintero

Motivated by the search for idempotent cellular automata (CA), we study CA that act almost as the identity unless they read a fixed pattern $p$ . We show that constant and symmetric…

math.GR2023★ 1 cited

Further results on generalized cellular automata

Alonso Castillo-Ramirez, Luguis de los Santos Baños

Given a finite set $A$ and a group homomorphism $ϕ : H \to G$ , a $ϕ$ -cellular automaton is a function $T : A^{G} \to A^{H}$ that is continuous with respect to the prodiscrete…

nlin.CG2023

A study on the composition of elementary cellular automata

Alonso Castillo-Ramirez, Maria G. Magaña-Chavez

Elementary cellular automata (ECA) are one-dimensional discrete models of computation with a small memory set that have gained significant interest since the pioneer work of Stephe…

math.GR2022★ 7 cited

A generalization of cellular automata over groups

A. Castillo-Ramirez, M. Sanchez-Alvarez, A. Vazquez-Aceves +1

Let $G$ be a group and let $A$ be a finite set with at least two elements. A cellular automaton (CA) over $A^{G}$ is a function $τ : A^{G} \to A^{G}$ defined via a finite memory set $S \s…

math.GR2022

The relative rank of the endomorphism monoid of a finite $G$ -set

Alonso Castillo-Ramirez, Ramón H. Ruiz-Medina

For a group $G$ acting on a set $X$ , let $End_{G} (X)$ be the monoid of all $G$ -equivariant transformations, or $G$ -endomorphisms, of $X$ , and let $Aut_{G} (X)$ be its grou…

math.GR2021★ 1 cited

The number of configurations in the full shift with a given least period

Alonso Castillo-Ramirez, Miguel Sánchez-Álvarez

For any group $G$ and any set $A$ , consider the shift action of $G$ on the full shift $A^{G}$ . A configuration $x \in A^{G}$ has \emph{least period} $H \leq G$ if the stabiliser of $x$ …

math.GR2020★ 3 cited

Generating infinite monoids of cellular automata

Alonso Castillo-Ramirez

For a group $G$ and a set $A$ , let $End (A^{G})$ be the monoid of all cellular automata over $A^{G}$ , and let $Aut (A^{G})$ be its group of units. By establishing a character…

math.GR2020★ 2 cited

Miyamoto groups of code algebras

Alonso Castillo-Ramirez, Justin McInroy

A code algebra $A_{C}$ is a nonassociative commutative algebra defined via a binary linear code $C$ . In a previous paper, we classified when code algebras are $Z_{2}$ -graded a…

math.GR2019★ 3 cited

On the minimal number of generators of endomorphism monoids of full shifts

Alonso Castillo-Ramirez

For a group $G$ and a finite set $A$ , denote by $End (A^{G})$ the monoid of all continuous shift commuting self-maps of $A^{G}$ and by $Aut (A^{G})$ its group of units. We st…

math.GR2019★ 4 cited

Cellular automata over algebraic structures

Alonso Castillo-Ramirez, O. Mata-Gutiérrez, Angel Zaldivar-Corichi

Let $G$ be a group and $A$ a set equipped with a collection of finitary operations. We study cellular automata $τ : A^{G} \to A^{G}$ that preserve the operations of $A^{G}$ induced compon…

math.GR2019

Bounding the minimal number of generators of groups and monoids of cellular automata

Alonso Castillo-Ramirez, Miguel Sanchez-Alvarez

For a group $G$ and a finite set $A$ , denote by $CA (G; A)$ the monoid of all cellular automata over $A^{G}$ and by $ICA (G; A)$ its group of units. We study the minimal ca…

math.GR2018★ 6 cited

Elementary, Finite and Linear vN-Regular Cellular Automata

Alonso Castillo-Ramirez, Maximilien Gadouleau

Let $G$ be a group and $A$ a set. A cellular automaton (CA) $τ$ over $A^{G}$ is von Neumann regular (vN-regular) if there exists a CA $σ$ over $A^{G}$ such that $τ σ τ = τ$ , and in such c…

math.RA2018★ 3 cited

Code algebras which are axial algebras and their $Z_{2}$ -gradings

Alonso Castillo-Ramirez, Justin McInroy

A code algebra $A_{C}$ is a non-associative commutative algebra defined via a binary linear code $C$ . We study certain idempotents in code algebras, which we call small idempotents,…

Coherent and dissipative coupling of multiple photon-magnon hybrids in a chiral microwave resonator

When do lazy and invertible cellular automata generate all cellular automata?

A characterization of the reversibility of linear cellular automata

Fusion rules from the Norton inequality

Topological Dynamics of Pullback Maps on Full Shifts

A categorical framework for cellular automata

On the order of lazy cellular automata

Categorical products of cellular automata

Connections between the minimal neighborhood and the activity value of cellular automata

One-dimensional cellular automata with a unique active transition

On the minimal memory set of cellular automata

Idempotent cellular automata and their natural order

Further results on generalized cellular automata

A study on the composition of elementary cellular automata

A generalization of cellular automata over groups

The relative rank of the endomorphism monoid of a finite G-set

The number of configurations in the full shift with a given least period

Generating infinite monoids of cellular automata

Miyamoto groups of code algebras

On the minimal number of generators of endomorphism monoids of full shifts

Cellular automata over algebraic structures

Bounding the minimal number of generators of groups and monoids of cellular automata

Elementary, Finite and Linear vN-Regular Cellular Automata

Code algebras which are axial algebras and their Z2​-gradings

The relative rank of the endomorphism monoid of a finite $G$ -set

Code algebras which are axial algebras and their $Z_{2}$ -gradings