相关论文: Minimal Finite Models

We organize a table of regular graphs with minimal diameters and minimal mean path lengths, large bisection widths and high degrees of symmetries, obtained by enumerations on supercomputers. These optimal graphs, many of which are newly…

We develop tame topology over dp-minimal structures equipped with definable uniformities satisfying certain assumptions. Our assumptions are enough to ensure that definable sets are tame: there is a good notion of dimension on definable…

Graphons are analytic objects associated with convergent sequences of graphs. Problems from extremal combinatorics and theoretical computer science led to a study of graphons determined by finitely many subgraph densities, which are…

A subset of vertices of a graph is minimal if, within all subsets of the same size, its vertex boundary is minimal. We give a complete, geometric characterization of minimal sets for the planar integer lattice X. Our characterization…

We prove:(1) the existence, for every integer n > 3, of a noncompact smooth n-dimensional topological manifold whose diffeomorphism group contains an isomorphic copy of every finitely presented group; (2) a finiteness theorem on finite…

We investigate various topological spaces and varieties which can be associated to a block of a finite group scheme G. These spaces come from the theory of cohomological support varieties for modules, as well as from the…

We present a diagram surveying equivalence or strict implication for properties of different nature (algebraic, model theoretic, topological, etc.) about groups definable in o-minimal structures. All results are well-known and an extensive…

Recently there has been growing interest in discrete homotopies and homotopies of graphs beyond treating graphs as 1-dimensional simplicial spaces. One such type of homotopy is $\times$-homotopy. Recent work by Chih-Scull has developed a…

We propose a new family of combinatorial inference problems for graphical models. Unlike classical statistical inference where the main interest is point estimation or parameter testing, combinatorial inference aims at testing the global…

Finite mixture models have been a very important tool for exploring complex data structures in many scientific areas, for example, economics, epidemiology, finance. In the past decade, semiparametric techniques have been popularly…

We apply the local removable singularity theorem for minimal laminations and the local picture theorem on the scale of topology to obtain two descriptive results for certain possibly singular minimal laminations of $\mathbb{R}^3$. These two…

The homological scaffold leverages persistent homology to construct a topologically sound summary of a weighted network. However, its crucial dependency on the choice of representative cycles hinders the ability to trace back global…

We develop a novel tool to study the fixed point property of finite posets using a topological approach. Our tool is a construction which turns out to induce an endofunctor of the homotopy category of finite $T_0$--spaces. We study many…

For Gamma a finite, connected metric graph, we consider the space of configurations of n points in Gamma with a restraint parameter r dictating the minimum distance allowed between each pair of points. These restricted configuration spaces…

In this paper, we classify all the finite groups $G$ such that the commuting graph $\Gamma_C(G)$, order-sum graph $\Gamma_{OS}(G)$ and non-inverse graph $\Gamma_{NI}(G)$ are minimally edge connected graphs. We also classify all the finite…

We classify all harmonic maps with finite uniton number from a Riemann surface into an arbitrary compact simple Lie group $G$, whether $G$ has trivial centre or not, in terms of certain pieces of the Bruhat decomposition of the group…

For digital images, there is an established homotopy equivalence relation which parallels that of classical topology. Many classical homotopy equivalence invariants, such as the Euler characteristic and the homology groups, do not remain…

We determine the homological residue fields, in the sense of tensor-triangular geometry, in a series of concrete examples ranging from topological stable homotopy theory to modular representation theory of finite groups.

Free actions of finite groups on spheres give rise to topological spherical space forms. The existence and classification problems for space forms have a long history in the geometry and topology of manifolds. In this article, we present a…

End-spaces of infinite graphs naturally generalise the Freudenthal boundary and sit at the interface between graph theory, geometric group theory and topology. Our main result is that every end-space can topologically be represented by a…