Related papers: Counting Finite Topologies

To facilitate widespread adoption of automated engineering design techniques, existing methods must become more efficient and generalizable. In the field of topology optimization, this requires the coupling of modern optimization methods…

We use a combinatorial approach to compute the number of non-isomorphic choices on four elements that can be explained by models of bounded rationality.

For every finite closure space $X$ one can define a finite topological space $\operatorname{Top} X$ together with a natural projection $\operatorname{Top} X\longrightarrow X$. This could allow to apply the techniques of topological…

Numerical methods: mimetic finite differences and finite elements, are analyzed from a numerical point of view. It seeks to conclude on the efficiency, order of convergence and computational cost of these methods. The analysis is done in…

We describe a theory of finite sets, and investigate the analogue of Dedekind's theory of natural number systems (simply infinite systems) in this theory. Unlike the infinitary case, in our theory, natural number systems come in differing…

This paper presents a combinatorial analog of topological complexity for finite spaces. We demonstrate that this coincides with the genuine topological complexity of the original finite space, and constitutes an upper bound for the…

We construct examples of nonresolvable generalized $n$-manifolds, $n\geq 6$, with arbitrary resolution obstruction, homotopy equivalent to any simply connected, closed $n$-manifold. We further investigate the structure of generalized…

We consider 9 natural tightness conditions for topological spaces that are all variations on countable tightness and investigate the interrelationships between them. Several natural open problems are raised.

We obtain the formula computing the number of isomorphic classes of element systems with characters over finite commutative group $G$.

We study finite morphisms of varieties and the link between their top multiplicity loci under certain assumptions. More precisely, we focus on how to determine that link in terms of the spaces of arcs of the varieties.

We give an upper bound for the number of points of a hypersurface over a finite field that has no lines on, in terms of the dimension, the degree, and the number of the elements of the finite field.

We consider ruled surfaces with finite multiplicity. We study behaviors of the striction curves and the singularities of the ruled surfaces. We also give geometric meanings of invariants related to the ruled surfaces.

In this paper, the author introduces the concept and basic properties of finite (commutative) hyperfields. Also, the author shows that, up to isomorphism, there are exactly 2 hyperfields of order 2; 5 hyperfields of order 3; 7 hyperfields…

In this short note we count the finite semirings up to isomorphism, and up to isomorphism and anti-isomorphism for some small values of $n$; for which we utilise the existing library of small semigroups in the GAP package Smallsemi.

New bounds on the number of similar or directly similar copies of a pattern within a finite subset of the line or the plane are proved. The number of equilateral triangles whose vertices all lie within an $n$-point subset of the plane is…

We characterize the fixed sets of automorphisms of an arbitrary countable, arithmetically saturated structure.

This is a survey on the finite basis problem for varieties of algebraic systems. Our exposition is in two directions: (i) We give numerous examples of varieties which are not finitely based. (ii) We give examples of important varieties with…

We estimate, in a number field, the number of elements and the maximal number of linearly independent elements, with prescribed bounds on their valuations. As a by-product, we obtain new bounds for the successive minima of ideal lattices.…

We prove that for any weakly convergent sequence of finite graphs with bounded vertex degrees, there exists a topological limit graphing.

A ringed finite space is a ringed space whose underlying topological space is finite. The category of ringed finite spaces contains, fully faithfully, the category of finite topological spaces and the category of affine schemes. Any ringed…