Related papers: Some questions on entangled linear orders

A vertex ordering of a graph $G$ is a bijection $\pi\colon\{1,\dots,|V(G)|\}\to V(G)$. It is successive if the induced subgraph $G[v_{\pi(1)},\dots,v_{\pi(k)}]$ is connected for each $k$. Lixing Fang, Hao Huang, J\'anos Pach, G\'abor…

A linear order $L$ is strongly surjective if $L$ can be mapped onto any of its suborders in an order preserving way. We prove various results on the existence and non-existence of uncountable strongly surjective linear orders answering…

In this paper we study the notion of first-order part of a computational problem, first introduced by Dzhafarov, Solomon, and Yokoyama, which captures the "strongest computational problem with codomain $\mathbb{N}$ that is Weihrauch…

Every invariant linear manifold for a CSL-algebra is a closed subspace if, and only if, each non-zero projection in the projection lattice is generated by finitely many atoms. In the case of a nest, this condition is equivalent to the…

Two finite Alexander quandles with the same number of elements are isomorphic iff their Z[t,t^-1]-submodules Im(1-t) are isomorphic as modules. This yields specific conditions on when Alexander quandles of the form Z_n[t,t^-1]/(t-a) where…

One of the most striking features of quantum phases that exhibit topological order is the presence of long range entanglement that cannot be detected by any local order parameter. The formalism of projected entangled-pair states is a…

J. Y. Hyun, et al. (Des. Codes Cryptogr., vol. 88, pp. 2475-2492, 2020) constructed some optimal and minimal binary linear codes generated by one or two order ideals in hierarchical posets of two levels. At the end of their paper, they left…

In this paper, we derive an optimal first-order Taylor-like formula. In a seminal paper [14], we introduced a new first-order Taylor-like formula that yields a reduced remainder compared to the classical Taylor's formula. Here, we relax the…

Any model of ZFC + GCH has a generic extension (made with a poset of size aleph_2) in which the following hold: MA + 2^{aleph_0}= aleph_2+ there exists a Delta^2_1-well ordering of the reals. The proof consists in iterating posets designed…

A reduced divisor on a nonsingular variety defines the sheaf of logarithmic 1-forms. We introduce a certain coherent sheaf whose double dual coincides with this sheaf. It has some nice properties, for example, the residue exact sequence…

The notion of lambda-symmetries, originally introduced by C. Muriel and J.L. Romero, is extended to the case of systems of first-order ODE's (and of dynamical systems in particular). It is shown that the existence of a symmetry of this type…

We elaborate on the deviation of the Jordan structures of two linear relations that are finite-dimensional perturbations of each other. We compare their number of Jordan chains of length at least $n$. In the operator case, it was recently…

The existence of an unbounded sequence of solutions to a conformally invariant elliptic equation having nonlocal critical-power nonlinearity is established. The primary obstacle to establishing existence of solutions is the failure of…

We study connections between linear equations over various semigroups and recursively enumerable sets of positive integers. We give variants of the universal Diophantine representation of recursively enumerable sets of positive integers…

We show that several classes of ordered structures (namely, convex linear orders, layered permutations, and compositions) admit first-order logical limit laws.

Yu. I. Merzljakov developed a method of splittable coordinates which helps to verify the linearity of some groups, he established some fundamental results using this method. In this paper we use the method of splittable coordinates and find…

This paper gives a new way of characterizing L-space $3$-manifolds by using orderability of quandles. Hence, this answers a question of Adam Clay et al. [Question 1.1 of Canad. Math. Bull. 59 (2016), no. 3, 472-482]. We also investigate…

We work out the unfolded formulation of the fields in the non-linear realisation of $E_{11}$. Using the connections in this formalism, we propose, at the linearised level, an infinite number of first-order duality relations between the dual…

Diekert, Matiyasevich and Muscholl proved that the existential first-order theory of a trace monoid over a finite alphabet is decidable. We extend this result to a natural class of trace monoids with infinitely many generators. As an…

In many nonlinear field theories, relevant solutions may be found by reducing the order of the original Euler-Lagrange equations, e.g., to first order equations (Bogomolnyi equations, self-duality equations, etc.). Here we generalise,…