Related papers: Representable posets

Based on the concept of weakly meet $s_{Z}$-continuouity put forward by Xu and Luo in \cite{qzm}, we further prove that if the subset system $Z$ satisfies certain conditions, a poset is $s_{Z}$-continuous if and only if it is weakly meet…

Given an abelian category with arbitrary products, arbitrary coproducts, and a generator, we show that the closed subspaces (in the sense of A. L. Rosenberg) are parameterized by a suitably defined poset of ideals in the generator. In…

We study the representations of a class of non-commutative polynomial algebras truncated at degree 3, with one additional relation. We determine the irreducible components of their varieties of representations. We do this by showing that…

Let $2<n<m\leq \omega$. Let $\CA_n$ denote the class of cylindric algebras of dimension $n$ and $\RCA_n$ denote the class of representable $\CA_n$s. We say that $\A\in \RCA_n$ is representable up to $m$ if $\Cm\At\A$ has an $m$-square…

We study periodic expansions in positional number systems with a base $\beta\in\C,\ |\beta|>1$, and with coefficients in a finite set of digits $\A\subset\C.$ We are interested in determining those algebraic bases for which there exists…

We introduce a new invariant for triangulated categories: the poset of spherical subcategories ordered by inclusion. This yields several numerical invariants, like the cardinality and the height of the poset. We explicitly describe…

In this paper we give a necessary and sufficient criterion for representability of a matroid over an algebraic closed field. This leads to an algorithm, based on an extension of Groebner Bases, in order to decide if a given matroid is…

A representation field for a non-maximal order $\Ha$ in a central simple algebra is a subfield of the spinor class field of maximal orders which determines the set of spinor genera of maximal orders containing a copy of $\Ha$. Not every…

Let $R$ be a semilocal principal ideal domain. Two algebraic objects over $R$ in which scalar extension makes sense (e.g. quadratic spaces) are said to be of the same genus if they become isomorphic after extending scalars to all…

We show a transfer principle for the property that all types realised in a given elementary extension are definable. It can be written as follows: a Henselian valued fields is stably embedded in an elementary extension if and only if its…

An unlabeled poset is said to be (2+2)-free if it does not contain an induced subposet that is isomorphic to 2+2, the union of two disjoint 2-element chains. Let $p_n$ denote the number of (2+2)-free posets of size $n$. In a recent paper,…

We investigate notions of complete representation by partial functions, where the operations in the signature include antidomain restriction and may include composition, intersection, update, preferential union, domain, antidomain, and set…

We consider extension of a closure system on a finite set S as a closure system on the same set S containing the given one as a sublattice. A closure system can be represented in different ways, e.g. by an implicational base or by the set…

Every partial applicative structure gives rise to an indexed binary relation, that is a contravariant functor from the category of sets to the category of sets endowed with binary relations and maps preserving them. In this paper we…

In standard methodology for natural language processing, entities in text are typically embedded in dense vector spaces with pre-trained models. The embeddings produced this way are effective when fed into downstream models, but they…

For a fixed finite dimensional algebra $A$, we study representation embeddings of the form $mod(B)\rightarrow mod(A)$. Such an embedding is called homological, if it induces an isomorphism on all Ext-groups and weakly homological, if only…

A few steps are made towards representation theory of embeddability among uncountable graphs. A monotone class of graphs is defined by forbidding countable subgraphs, related to the graph's end-structure. Using a combinatorial theorem of…

Representable implication algebras are known to be axiomatised by a finite number of equations (making the representation and finite representation problems decidable here). We show that this also holds in the context of unary (and binary)…

We classify irreducible representations of connected compact Lie groups whose orbit space is isometric to the orbit space of a representation of a finite extension of (positive dimensional) toric group. They turn out to be exactly the…

We give a characterisation of representation-finite symmetric algebras of period four, and describe their basic algebras. In particular, if such an algebra is indecomposable, it has at most two simple modules.