Related papers: Musical Systems with $\mathbb{Z}_n$ -- Cayley Grap…

Music genre classification shapes how listeners discover music, how platforms design recommendations, and how sociologists study cultural taste. Yet existing genre labels are inconsistent in granularity: they exaggerate boundaries between…

A harmonic mapping is a univalent harmonic function of one complex variable. We define a family of harmonic mappings on the unit disk whose images are rotationally symmetric rosettes with $n$ cusps or n nodes, where $n \ge 3$. These…

We introduce a new model for investigating spectral properties of quantum graphs, a quantum circulant graph. Circulant graphs are the Cayley graphs of cyclic groups. Quantum circulant graphs with standard vertex conditions maintain…

We construct a 2-generated group $\Gamma $ such that its Cayley graph possesses finite connected subsets with arbitrarily big finite Heesch number.

Computational models of music, while providing good descriptions of melodic development, still cannot fully grasp the general structure comprised of repetitions, transpositions, and reuse of melodic material. We present a corpus of strongly…

In this paper, generalizing the result in \cite{GXY}, we construct strongly regular Cayley graphs by using union of cyclotomic classes of $\F_q$ and Gauss sums of index $w$, where $w\geq 2$ is even. In particular, we obtain three infinite…

For a postive integer $n$ and a subset $S$ of $\mathbb{Z}_n$, let $\left\langle S\right\rangle =\mathbb{Z}_n$, and $w:S\rightarrow\mathbb{N}$ be a function. The weighted Cayley graph of the cyclic group $\mathbb{Z}_n$ with respect to $S$…

We demonstrate how contact chord diagrams can arise from certain Fock-space models and compute the corresponding correlation functions using the chord path integral technique. In particular, our three-point functions are in the right form…

A graph is chordal if every cycle of length at least four contains a chord, that is, an edge connecting two nonconsecutive vertices of the cycle. Several classical applications in sparse linear systems, database management, computer vision,…

Let us denote elements of the symmetric group $S_n$ using square brackets for the one-line notation. Cycles will be represented using parentheses, following the standard cycle notation. Under this convention, the full reversal of the…

We define the Cayley graph and its growth function for multivalued groups. We prove that if we change a finite set of generators of multivalued group, or change the starting point, we get an equivalent growth function. We prove that if we…

In this paper we study finite groups which have Cayley isomorphism property with respect to Cayley maps, CIM-groups for a brief. We show that the structure of the CIM-groups is very restricted. It is described in Theorem~\ref{111015a} where…

We prove various properties on the structure of groups whose power graph is chordal. Nilpotent groups with this property have been classified by Manna, Cameron and Mehatari [The Electronic Journal of Combinatorics, 2021]. Here we classify…

In recent years, artificial neural networks (ANNs) have become a universal tool for tackling real-world problems. ANNs have also shown great success in music-related tasks including music summarization and classification, similarity…

We describe the inverse image of the Riemannian exponential map at a basepoint of a compact symmetric space as the disjoint union of so called focal orbits through a maximal torus. These are orbits of a subgroup of the isotropy group acting…

Many systems comprising entities in interactions can be represented as graphs, whose structure gives significant insights about how these systems work. Network theory has undergone further developments, in particular in relation to…

We show that groups presented by inverse-closed finite convergent length-reducing rewriting systems are characterised by a striking geometric property: their Cayley graphs are geodetic and side-lengths of non-degenerate triangles are…

Convex geometries are closure systems satisfying the anti-exchange axiom. Every finite convex geometry can be embedded into a convex geometry of finitely many points in an n-dimensional space equipped with a convex hull operator, by the…

The subjective quality of natural signals can be approximated with objective perceptual metrics. Designed to approximate the perceptual behaviour of human observers, perceptual metrics often reflect structures found in natural signals and…

The aim of this study is to teach an algorithm how to recognize different types of music. Users will submit songs for analysis. Since the algorithm hasn't heard these songs before, it needs to figure out what makes each song unique. It does…