相关论文: (M + 1)-step shift spaces that are not conjugate t…

We provide a characterization of $J$-class and $J^{mix}$-class unilateral weighted shifts on $l^{\infty}(\mathbb{N})$ in terms of their weight sequences. In contrast to the previously mentioned result we show that a bilateral weighted shift…

We study the dynamical properties of certain shift spaces. To help study these properties we introduce two new classes of shifts, namely boundedly supermultiplicative (BSM) shifts and balanced shifts. It turns out that any almost specified…

Two cellular automata are strongly conjugate if there exists a shift-commuting conjugacy between them. We prove that the following two sets of pairs $(F,G)$ of one-dimensional one-sided cellular automata over a full shift are recursively…

We introduce two algebras associated with a subshift over an arbitrary alphabet. One is unital and the other not necessarily. We focus on the unital case and describe a conjugacy between Ott-Tomforde-Willis subshifts in terms of a…

We define a new class of shift spaces which contains a number of classes of interest, like Sturmian shifts used in discrete geometry. We show that this class is closed under two natural transformations. The first one is called conjugacy and…

In this paper, we explore the construction and dynamical properties of $\mathcal{S}$-limited shifts. An $S$-limited shift is a subshift defined on a finite alphabet $\mathcal{A} = \{1, \ldots,p\}$ by a set $\mathcal{S} = \{S_1, \ldots,…

One way to construct a maximal set of mutually unbiased bases (MUBs) in a prime-power dimensional Hilbert space is by means of finite phase-space methods. MUBs obtained in this way are covariant with respect to some subgroup of the group of…

We construct an infinite word $w$ over the $5$-letter alphabet such that for every factor $f$ of $w$ of length at least two, there exists a cyclic permutation of $f$ that is not a factor of $w$. In other words, $w$ does not contain a…

We introduce a new type of shift dynamics as an extended model of symbolic dynamics, and investigate the characteristics of shift spaces from the viewpoints of both dynamics and computation. This shift dynamics is called a functional shift…

Let $ X_{\beta}$ be a sofic $ \beta $-shift for $ \beta \in (1, 2] $. We show that there is an $ S $-gap shift $ X(S) $ such that $ X_{\beta} $ and $ X(S) $ are right-resolving almost conjugate. Conversely, a condition on $ S \subseteq…

We study some basic properties of sofic-Dyck shifts and finite-type-Dyck shifts. We prove that the class of sofic-Dyck shifts is stable under proper conjugacies. We prove a Decomposition Theorem of a proper conjugacy between edge-Dyck…

We consider the multiplicative structure of sets of the form AA+1, where where A is a large, finite set of real numbers. In particular, we show that the additively shifted product set, AA+1 must have a large part outside of any generalized…

We study the automorphism group of an infinite minimal shift $(X,\sigma)$ such that the complexity difference function, $p(n+1)-p(n)$, is bounded. We give some new bounds on $\mbox{Aut}(X,\sigma)/\langle \sigma \rangle$ and also study the…

We prove that a unital shift equivalence induces a graded isomorphism of Leavitt path algebras when the shift equivalence satisfies an alignment condition. This yields another step towards confirming the Graded Classification Conjecture.…

In this work we characterize those shift spaces which can support a 1-block quasi-group operation and show the analogous of Kitchens result: any such shift is conjugated to a product of a full shift with a finite shift. Moreover, we prove…

We present a collection of results concerning the structure of reversible gate classes over non-binary alphabets, including (1) a reversible gate class over non-binary alphabets that is not finitely generated (2) an explicit set of…

Using follower/predecessor/extender set sequences, we define quantities which we call the follower/predecessor/extender entropies, which can be associated to any shift space. We analyze the behavior of these quantities under conjugacies and…

Let $G$ be a finitely generated amenable group. We study the space of shifts on $G$ over a given finite alphabet $A$. We show that the zero entropy shifts are generic in this space, and that more generally the shifts of entropy $c$ are…

The periodic (ordinal) patterns of a map are the permutations realized by the relative order of the points in its periodic orbits. We give a combinatorial characterization of the periodic patterns of an arbitrary signed shift, in terms of…

Higher-dimensional binary shifts of number-theoretic origin with positive topological entropy are considered. We are particularly interested in analysing their symmetries and extended symmetries. They form groups, known as the topological…