Related papers: Association Scheme on Triples from the Unitary Gro…
A square trisection is a problem of assembling three identical squares from a larger square, using a minimal number of pieces. This paper presents an historical overview of the square trisection problem starting with its origins in the…
We continue our study of string correlators on Euclidean $\text{AdS}_3$ with pure NS-NS flux. The worldsheet and spacetime correlators have a rich analytic structure, which we analyse completely for genus 0 four-point functions. We show…
A "biased expansion" of a graph is a kind of branched covering graph with additional structure related to combinatorial homotopy of circles. Some but not all biased expansions are constructed from groups ("group expansions"); these include…
Scaffolds are certain tensors arising in the study of association schemes, and have been (implicitly) understood diagrammatically as digraphs with distinguished "root" nodes and with matrix edge weights, often taken from Bose-Mesner…
In this paper, we define a class of auxiliary graphs associated with simple undirected graphs. This class of auxiliary graphs is based on the set of spanning trees of the original graph and the edges constituting those spanning trees. A…
A representation of the Dirac algebra, derived from first principles, can be related to the combinations of unit charges which determine particle structures. The algebraic structure derives from a broken symmetry between 4-vectors and…
Graph association rule mining is a data mining technique used for discovering regularities in graph data. In this study, we propose a novel concept, {\it path association rule mining}, to discover the correlations of path patterns that…
For a mixing shift of finite type, the associated automorphism group has a rich algebraic structure, and yet we have few criteria to distinguish when two such groups are isomorphic. We introduce a stabilization of the automorphism group,…
The distance of an operation from being associative can be "measured" by its associative spectrum, an appropriate sequence of positive integers. Associative spectra were introduced in a publication by B. Cs\'ak\'any and T. Waldhauser in…
We introduce the triple crossing number, a variation of crossing number, of a graph, which is the minimal number of crossing points in all drawings with only triple crossings of the graph. It is defined to be zero for a planar graph, and to…
Transition graphs capture the memory and sequential response of multistable media, by specifying their evolution under external driving. Microscopically, collections of bistable elements, or hysterons, provide a powerful model for these…
A triple chord is a sub-diagram of a chord diagram that consists of a circle and finitely many chords connecting the preimages for every double point on a spherical curve, and it has exactly three chords giving the triple intersection. This…
In this paper, we construct directed strongly regular graphs and divisible design graphs with new parameters merging some basic relations of so-called Tatra associations schemes. We also study the above association schemes, their fusions…
Altanisation (formation of the altan of a parent structure) originated in the chemical literature as a formal device for constructing generalised coronenes from smaller structures. The altan of graph $G$, denoted $\mathfrak{a}(G, H)$,…
Several methods for generating random Steiner triple systems (STSs) have been proposed in the literature, such as Stinson's hill-climbing algorithm and Cameron's algorithm, but these are not yet completely understood. Those algorithms, as…
A compatible associative algebra is a vector space endowed with two associative multiplication operations that satisfy a natural compatibility condition. In this paper, we investigate and classify compatible pairs of associative algebras of…
We provide a general program for finding nice arrangements of points in real or complex projective space from transitive actions of finite groups. In many cases, these arrangements are optimal in the sense of maximizing the minimum…
We give a description of the link between topological dynamical systems and their dimension groups. The focus is on minimal systems and, in particular, on substitution shifts. We describe in detail the various classes of systems including…
In this paper we develop a structure called Link Algebra, in which we present a Set with two binary operations and an axiom system developed from the study of graph theory and set/antiset theory, sowing main theorems and definitions. Once…
A Latin square of order $n$ with symbols $a_1,\ldots,a_n$ can be considered as a multiplication table for binary operation in the set $A=\{a_1,\ldots,a_n\}$. We prove that, if this operation is associative, then $A$ is a group.