Related papers: Reversibility of Extreme Relational Structures
In this paper we provide an overview of the class of inverse semigroups $S$ such that every congruence on $S$ relates at least one idempotent to a non-idempotent; such inverse semigroups are called $E$-disjunctive. This overview includes…
We say that an ideal I is homogeneous, if its restriction to any I-positive subset is isomorphic to I. The paper investigates basic properties of this notion -- we give examples of homogeneous ideals and present some applications to…
Suppose a finite group acts on a scheme X and a finite-dimensional Lie algebra g. The corresponding equivariant map algebra is the Lie algebra M of equivariant regular maps from X to g. We classify the irreducible finite-dimensional…
We give an overview of some properties of Lie algebras generated by at most 5 extremal elements. In particular, for any finite graph {\Gamma} and any field K of characteristic not 2, we consider an algebraic variety X over K whose K-points…
An arbitrary dependence structure between a finite family of events of a probability space defines a hypergraph structure. We study the converse operation, starting from a hypergraph structure, to determine a canonical probability space…
We investigate the complexity of isomorphism relations for classes of finitely generated and n-generated computably enumerable (c.e.) algebras, presented via c.e. presentations -- that is, as quotients of term algebras over decidable sets…
We introduce a reducibility on classes of structures, essentially a uniform enumeration reducibility. This reducibility is inspired by the Friedman-Stanley paper on using Borel reductions to compare classes of countable structures. This…
If $(X, \le_X)$ is a partially ordered set satisfying certain necessary conditions for $X$ to be order-isomorphic to the spectrum of a Noetherian domain of dimension two, we describe a new poset $(\text{str } X, \le_{\text{str } X})$ that…
The symmetric inverse semigroup $I(X)$ on a set $X$ is the collection of all partial bijections between subsets of $X$ with composition as the algebraic operation. We study a minimal Hausdorff inverse semigroup topologies on $I(X)$. When…
Louveau and Rosendal [5] have shown that the relation of bi-embeddability for countable graphs as well as for many other natural classes of countable structures is complete under Borel reducibility for analytic equivalence relations. This…
For a bivariate random vector (X,Y), symmetry conditions are presented that yield stochastic orderings among |X|, |Y|, |max(X,Y)|, and | min(X, Y)|. Partial extensions of these results for multivariate random vectors (X1,...,Xn) are also…
Recursive queries have been traditionally studied in the framework of datalog, a language that restricts recursion to monotone queries over sets, which is guaranteed to converge in polynomial time in the size of the input. But modern big…
We find necessary and sufficient conditions on an (inverse) semigroup $X$ under which its semigroups of maximal linked systems $\lambda(X)$, filters $\phi(X)$, linked upfamilies $N_2(X)$, and upfamilies $\upsilon(X)$ are inverse.
An orthoset (also called an orthogonality space) is a set $X$ equipped with a symmetric and irreflexive binary relation $\perp$, called the orthogonality relation. In quantum physics, orthosets play a central role. In fact, a Hilbert space…
When n is odd, consider the finite general linear and unitary groups of rank n, extended by the inverse transpose automorphism. There are elements in the extended groups which square to a regular unipotent element, and we evaluate the…
We study continuous homomorphisms between algebras of iterated Laurent series over a commutative ring. We give a full description of such homomorphisms in terms of a discrete data determined by the images of parameters. In similar terms, we…
A structure is called weakly oligomorphic if it realizes only finitely many n-ary positive existential types for every n. The goal of this paper is to show that the notions of homomorphism-homogeneity, and weak oligomorphy are not only…
We study pseudorandomness and pseudorandom generators from the perspective of logical definability. Building on results from ordinary derandomization and finite model theory, we show that it is possible to deterministically construct, in…
We prove that the universal homogeneous 3-uniform hypergraph has finite big Ramsey degrees. This is the first case where big Ramsey degrees are known to be finite for structures in a non-binary language. Our proof is based on the vector (or…
Much research has studied foundations for correct and reliable communication-centric systems. A salient approach to correctness uses session types to enforce structured communications; a recent approach to reliability uses reversible…