arXiv subjects

Carlos Correia Ramos

Publications and source records attributed to Carlos Correia Ramos.

4 recordsLinked to original sources

arXiv2026

Decomposable shuffles

We develop a combinatorial and order-theoretic framework for shuffles, understood as ordered concatenations of indexed families of sequences that induce total orders on the natural numbers. Motivated by the classical Šarkovskiĭ order, we introduce elementary building blocks that encode finite and infinite order patterns and focus on decomposable shuffles constructed from finite ordinals together with $ω$ and its dual $ω^*$. We define representations that allow individual elements to be located within a shuffle and show how suitable structural conditions yield total orders on $\mathbb{N}$

math.CO↗

arXiv2022

Unifying interval maps and branching systems with applications to relative graph C*-algebras

We describe Markov interval maps via branching systems and develop the theory of relative branching systems, characterizing when the associated representations of relative graph C*-algebras are faithful. When the Markov interval maps $f$ have escape sets, we use our results to characterize injectivity of the associated relative graph algebra representations, improving on previous work by the first, third, and fourth authors.

math.OA↗

arXiv2018

On graph algebras from interval maps

We produce and study a family of representations of relative graph algebras on Hilbert spaces that arise from the orbits of points of one dimensional dynamical systems, where the underlying Markov interval maps $f$ have escape sets. We identify when such representations are faithful in terms of the transitions to the escape subintervals.

math.OA↗

arXiv2012

Orbit Representations from Linear mod 1 Transformations

We show that every point $x_0\in [0,1]$ carries a representation of a $C^*$-algebra that encodes the orbit structure of the linear mod 1 interval map $f_{β,α}(x)=βx +α$. Such $C^*$-algebra is generated by partial isometries arising from the subintervals of monotonicity of the underlying map $f_{β,α}$. Then we prove that such representation is irreducible. Moreover two such of representations are unitarily equivalent if and only if the points belong to the same generalized orbit, for every $α\in [0,1[$ and $β\geq 1$.

math.OA↗