相关论文: Closures and generating sets related to combinatio…
Given a multiplicatively closed subset $S$ of the integers, there exist Structure Theorems for $LC$ modules over the localization $\mathbb{Z}S^{-1}$ that are "similar" to those of $LCA$ groups. The most notable one is the 1st Theorem: Given…
We study properties of classes of closure operators and closure systems parameterized by systems of isotone Galois connections. The parameterizations express stronger requirements on idempotency and monotony conditions of closure operators.…
A language L is low for a relativizable complexity class C, if C$^L$ = C. For the classes #P, GapP, and SpanP the exact low classes of languages are known: Low(#P) = UP $\cap$ coUP, Low(GapP) = SPP, and Low(SpanP) = NP $\cap$ coNP. In this…
Every bounded definable open set is a union of finitely many open strong cells in a weakly o-minimal expansion of a real closed field. We prove this fact and another theorem similar to it.
In this article we introduce a definition of topological minimal sets, which is a generalization of that of Mumford-Shah-minimal sets. We prove some general properties as well as two existence theorems for topological minimal sets. As an…
Generating trees are a useful technique in the enumeration of various combinatorial objects, particularly restricted permutations. Quite often the generating tree for the set of permutations avoiding a set of patterns requires infinitely…
Preservation theorems provide a direct correspondence between the syntactic structure of first-order sentences and the closure properties of their respective classes of models. A line of work has explored preservation theorems relativised…
We study the problem of fitting ontologies and constraints to positive and negative examples that take the form of a finite relational structure. As ontology and constraint languages, we consider the description logics $\mathcal{E\mkern-2mu…
Given a poset $P$ and a standard closure operator $\Gamma:\wp(P)\to\wp(P)$ we give a necessary and sufficient condition for the lattice of $\Gamma$-closed sets of $\wp(P)$ to be a frame in terms of the recursive construction of the…
The generating graph encodes how generating pairs are spread among the elements of a group. For more than ten years it has been conjectured that this graph is connected for every finite group. In this paper, we give evidence supporting this…
We investigate the extent to which the exchange relation holds in finite groups $G$. We define a new equivalence relation $\equiv_{\mathrm{m}}$, where two elements are equivalent if each can be substituted for the other in any generating…
We study the combinatorial and structural properties of the circle map sequences. We introduce an embedding procedure which gives a map from the hull(closure of the set of translates) to the sequence of embedding operations through which we…
This paper generalizes the basic notions of additive and multiplicative combinatorics to the setting of group actions: if $G$ is a group acting on a set $X$, and we have subsets $A\subseteq G$ and $Y\subseteq X$ such that the set of pairs…
Certain operator algebras A on a Hilbert space have the property that every densely defined linear transformation commuting with A is closable. Such algebras are said to have the closability property. They are important in the study of the…
We study approximations of theories both in general context and with respect to some natural classes of theories. Some kinds of approximations are considered, connections with finitely axiomatizable theories and minimal generating sets of…
The invariant theory of finite groups can connect the coding theory to the number theory. In this paper, under this conformity, we obtain the minimal generators of the rings of E-polynomials constructed from the groups related to…
We determine whether each known generating set of arbitrary oriented Reidemeister moves is minimal. We then provide a complete classification of minimal generating sets that include a coherent Reidemeister move of type II. We also classify…
Existentially closed groups are, informally, groups that contain solutions to every consistent finite system of equations and inequations. They were introduced in 1951 in an algebraic context and subsequent research elucidated deep…
We introduce a notion of compatibility between constraint encoding and compositional structure. Phrased in the language of category theory, it is given by a "composable constraint encoding". We show that every composable constraint encoding…
It is a striking fact from reverse mathematics that almost all theorems of countable and countably representable mathematics are equivalent to just five subsystems of second order arithmetic. The standard view is that the significance of…