Related papers: Triplets of Tri-Homological Triangles

This paper deals with the celebrated Euclidean theorem about isosceles triangles, comparing different proofs.

We study triangle decompositions of graphs. We consider constructions of classes of graphs where every edge lies on a triangle and the addition of the minimum number of multiple edges between already adjacent vertices results in a strongly…

We prove a triangulation theorem for semi-algebraic sets over a p-adically closed field, quite similar to its real counterpart. We derive from it several applications like the existence of flexible retractions and splitting for…

A combinatorial group-theoretic hypothesis is presented that serves as a necessary and sufficient condition for a union of connected Cockcroft two-complexes to be Cockcroft. This hypothesis has a component that can be expressed in terms of…

A general construction yielding infinitely many families of $D(m^2)$-triples of triangular numbers is presented. Moreover, each triple obtained from this construction contains the same triangular number $T_n$.

This article is devoted to the properties of the planar triangulations. The conjugated planar triangulation will be introduced and on the base of the properties, which were achieved by the other authors there will be proved some theorems,…

Two triples of triangles having pairwise disjoint outlines in 3-space are called combinatorially isotopic if one triple can be obtained from the other by a continuous motion during which the outlines of the triangles remain pairwise…

We establish a simple generalization for the famous theorem of Morley about trisectors in triangle with a purely synthetic proof using only angle chasing and similar triangles. Furthermore, based on the converse construction, another simple…

In this paper, we prove certain theorems about three consecutive primes.

We construct a new family of skein exact triangles for link Floer homology. The skein triples are described by a triple of rational tangles $(R_0,R_1,R_{2n+1})$, where $R_0$ is the trivial tangle and $R_k$ is obtained from it by applying…

The conditions determining that two triangles are congruent play a basic role in planimetry. By comparing not congruent triangles with respect to given sets of corresponding elements it is important to discover if they have any common…

We prove that a certain homological epimorphism between two algebras induces a triangle equivalence between their singularity categories. Applying the result to a construction of matrix algebras, we describe the singularity categories of…

Starting from any given rational-sided, right triangle, for example the $(3,4,5)$-triangle with area $6$, we use Euclidean geometry to show that there are infinitely many other rational-sided, right triangles of the same area. We show…

This thesis develops the theory of bundle gerbes and examines a number of useful constructions in this theory. These allow us to gain a greater insight into the structure of bundle gerbes and related objects. Furthermore they naturally lead…

The paper concerns the cohomology of (multiplicative) BiHom-associative trialgebras. We first detail the correspondence between central extensions and second cohomology. This is followed by a general cohomology theory that unifies those of…

The aim of this work is to use Napoleon's Theorem in different regular polygons, and decide whether we can prove Napoleon's Theorem is only limited with triangles or it could be done in other regular polygons that can create regular…

We calculate the Heegaard Floer homologies for three-manifolds obtained by plumbings of spheres specified by certain graphs. Our class of graphs is sufficiently large to describe, for example, all Seifert fibered rational homology spheres.…

This article has been written for an educational magazine whose target audience consists of students and teachers of mathematics in universities, colleges and schools. It concerns a notion of duality between rectangles. A proof is given…

In this note, we outline the general development of a theory of symmetric homology of algebras, an analog of cyclic homology where the cyclic groups are replaced by symmetric groups. This theory is developed using the framework of crossed…

We prove dual theorems to theorems proved by author in \cite {5}. Beginning with Section 10, we introduce and study so-called "twin numbers of the second kind" and a postulate for them. We give two proofs of the infinity of these numbers…