Related papers: Bounding, splitting, and almost disjointness
An alternating distance is a link invariant that measures how far away a link is from alternating. We study several alternating distances and demonstrate that there exist families of links for which the difference between certain…
Let $Y$ and $Z$ be two fixed topological spaces and $C(Y,Z)$ the set of all continuous maps from $Y$ into $Z$. We construct and study topologies on $C(Y,Z)$ that we call ${\cal F}_n(\tau_n)$-family-open topologies. Furthermore, we find…
This article investigates structural connections between unrefinable partitions into distinct parts and numerical semigroups. By analysing the hooksets of Young diagrams associated with numerical sets, new criteria for recognising…
A graph drawing in the plane is called an almost embedding if the images of any two non-adjacent simplices (i.e. vertices or edges) are disjoint. Almost embeddings (more precisely, their higher-dimensional analogues) naturally appear in…
We introduce two families of inequalities. Large ensemble decoupling is connected to the continuous restriction phenomenon. Tight decoupling is connected to the discrete Restriction conjecture for the sphere. Our investigation opens new…
We generalize the joints problem to sets of varieties and prove almost sharp bound on the number of joints. As a special case, given a set of $N$ $2$-planes in $\mathbb{R}^6$, the number of points at which three $2$-planes intersect and…
We give a sufficient condition for an almost alternating link diagram to represent a non-splittable link. The main theorem gives us a way to see if a given almost alternating link diagram represents a splittable link without increasing…
The aim of this paper is to present the main constructions of the substructures of an almost groupoid and to discuss their basic properties. The definitions and properties concerning these new algebraic constructions extend to almost…
In this paper, we investigate a novel form of approximate orthogonality that is based on integral orthogonality. Additionally, we establish the fundamental properties of this new approximate orthogonality and examine its capability to…
We characterize a family of number triangles whose production matrices are closely related to the original number triangle. We study a number of such triangles that are of combinatorial significance. For a specific subfamily, these…
We consider quasiconformal deformations of $\mathbb{C}\setminus\mathbb{Z}$. We give some criteria for infinitely often punctured planes to be quasiconformally equivalent to $\mathbb{C}\setminus\mathbb{Z}$. In particular, we characterize the…
In this short survey we review recent results dealing with algebraic structures (quandles, psyquandles, and singquandles) related to singular knot theory. We first explore the singquandles counting invariant and then consider several recent…
Binary multirelations generalise binary relations by associating elements of a set to its subsets. We study the structure and algebra of multirelations under the operations of union, intersection, sequential and parallel composition, as…
This paper provides fascinating connections between several mathematical problems which lie on the intersection of several mathematics subjects, namely algebraic geometry, approximation theory, complex-harmonic analysis and high dimensional…
We explore the notion of degree of asymmetry for integer sequences and related combinatorial objects. The degree of asymmetry is a new combinatorial statistic that measures how far an object is from being symmetric. We define this notion…
Structures of commuting semigroups of isometries under certain additional assumptions like double commutativity or dual double commutativity are found.
We answer a question from Raghavan and Stepr{\=a}ns' paper on weakly tight families by showing that $\mathfrak{s} = {\mathfrak{s}}_{\omega, \omega}$. Then we use this to construct a completely separable maximal almost disjoint family under…
We study the distribution of arithmetic invariants associated to Alexander polynomials for certain infinite families of links. The families of links we consider arise from braids on a fixed number of strings. We explore analogies with…
We present new proofs for some summation identities involving Stirling numbers of both first and second kind. The two main identities show a connection between Stirling numbers and Bessel numbers. Our method is based on solving a particular…
We investigate the partial orderings of the form (P(X),\subset), where X is a relational structure and P(X) the set of the domains of its isomorphic substructures. A rough classification of countable binary structures corresponding to the…