Related papers: On Derivatives and Subpattern Orders of Countable …

We study monitorable sets from a topological standpoint. In particular, we use descriptive set theory to describe the complexity of the family of monitorable sets in a countable space $X$. When $X$ is second countable, we observe that the…

In this paper we present a systematic study of continuous local iterated function systems. We prove local iterated function systems admit compact attractors and, under a contractivity assumption, construct their code space and present an…

We initiate the classification of unitary superconformal defects in unitary superconformal field theories (SCFT) of diverse spacetime dimensions $3\leq d \leq 6$. Our method explores general constraints from the defect superconformal…

Given a factor code between sofic shifts X and Y, there is a family of decompositions of the original code into factor codes such that the entropies of the intermediate subshifts arising from the decompositions are dense in the interval…

In this work, we prove that every SFT, sofic shift, and strongly irreducible shift on locally finite groups has strong dynamical properties. These properties include that every sofic shift is an SFT, every SFT is strongly irreducible, every…

In this paper we study the 2-dimension of a finite poset from the topological point of view. We use homotopy theory of finite topological spaces and the concept of a beat point to improve the classical results on 2-dimension, giving a more…

We prove that the lamplighter group admits strongly aperiodic SFTs, has undecidable tiling problem, and the entropies of its SFTs are exactly the upper semicomputable nonnegative real numbers, and some other results. These results follow…

Consider $d$ disjoint closed subintervals of the unit interval and consider an orientation preserving expanding map which maps each of these subintervals to the whole unit interval. The set of points where all iterates of this expanding map…

We characterize the finite distributive lattices which admit a complete valuation, that is bijective over a set of consecutive natural numbers, with the additional conditions of completeness (Definition 2.3). We prove that such lattices are…

We investigate multi-field multicritical scalar theories using CFT constraints on two- and three-point functions combined with the Schwinger-Dyson equation. This is done in general and without assuming any symmetry for the models, which we…

For any infinite subset $X$ of the rationals and a subset $F \subseteq X$ which has no isolated points in $X$ we construct a function $f: X \to X$ such that $f(f(x))=x$ for each $x\in X$ and $F $ is the set of discontinuity points of $f$.

Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…

Finite-order invariants of knots in arbitrary 3-manifolds (including non-orientable ones) are constructed and studied by methods of the topology of discriminant sets. Obstructions to the integrability of admissible weight systems to…

Countable tightness may be destroyed by countably closed forcing. We characterize the indestructibility of countable tightness under countably closed forcing by combinatorial statements similar to the ones Tall used to characterize…

Generalized dualities had an intriguing incursion into Double Field Theory (DFT) in terms of local $O(d,d)$ transformations. We review this idea and use the higher derivative formulation of DFT to compute the first order corrections to…

We investigate the partial orderings of the form (P(X),\subset), where X is a countable binary relational structure and P(X) the set of the domains of its isomorphic substructures and show that if the components of X are maximally…

For countably infinite IFSs on $\mathbb R^2$ consisting of affine contractions with diagonal linear parts, we give conditions under which the affinity dimension is an upper bound for the Hausdorff dimension and a lower bound for the lower…

We construct a nontrivial three-dimensional subshift of finite type whose projective $\Z$-subdynamics, or $\Z$-trace, is 2-sparse, meaning that there are at most two nonzero symbols in any vertical column. The subshift is deterministic in…

We consider D1-D5-P states in the untwisted sector of the D1-D5 orbifold CFT where we excite one copy of the seed CFT with a left-moving superconformal descendant. When the theory is deformed away from this region of moduli space these…

Let $X$ be a $2$-dimensional subshift of finite type generated by a finite set of forbidden blocks (of finite size). We give an algorithm for generating the elements of the shift space using sequence of finite matrices (of increasing size).…