Related papers: Association schemes and orthogonality graphs on an…
An association scheme is called partially metric if it has a connected relation whose distance-two relation is also a relation of the scheme. In this paper we determine the symmetric partially metric association schemes with a multiplicity…
Non-Hermitian degeneracies, also known as exceptional points (EPs), have been the focus of much attention due to their singular eigenvalue surface structure. Nevertheless, as pertaining to a non-Hermitian metasurface platform, the reduction…
Classical finite association schemes lead to a finite-dimensional algebras which are generated by finitely many stochastic matrices. Moreover, there exist associated finite hypergroups. The notion of classical discrete association schemes…
Degeneracy points in non-Hermitian systems are of great interest. While a homotopic framework exists for understanding their behavior in the absence of symmetry, it does not apply to symmetry-protected degeneracy points with reduced…
We give a description of the Hochschild cohomology for noncommutative planes (resp. quadrics) using the automorphism groups of the elliptic triples (resp. quadruples) that classify the Artin-Schelter regular $\mathbb{Z}$-algebras used to…
This semi-expository paper surveys results concerning three classes of orthogonal polynomials: in one non-hermitian variable, in several isometric non-commuting variables, and in several hermitian non-commuting variables. The emphasis is on…
Fiol has characterized quotient-polynomial graphs as precisely the connected graphs whose adjacency matrix generates the adjacency algebra of a symmetric association scheme. We show that a collection of non-negative integer parameters of…
We study the equivalence between bipartiteness and symmetry of spectra of mixed graphs, for $\theta$-Hermitian adjacency matrices defined by an angle $\theta \in (0, \pi]$. We show that this equivalence holds when, for example, an angle…
In this paper we consider partial linear spaces induced on the point set of a polar space, but with as lines the hyperbolic lines of this polar space. We give some geometric characterizations of these and related spaces. The results have…
A $k$-polar Grassmannian is the geometry having as pointset the set of all $k$-dimensional subspaces of a vector space $V$ which are totally isotropic for a given non-degenerate bilinear form $\mu$ defined on $V.$ Hence it can be regarded…
We study harmonic morphisms of graphs as a natural discrete analogue of holomorphic maps between Riemann surfaces. We formulate a graph-theoretic analogue of the classical Riemann-Hurwitz formula, study the functorial maps on Jacobians and…
In this work we deal with a scalar spectral mixed boundary value problem in a spacial junction of thin rods and a plate. Constructing asymptotics of the eigenvalues, we employ two equipollent asymptotic models posed on the skeleton of the…
Let $\Gamma=\Gamma(2n,q)$ be the dual polar graph of type $Sp(2n,q)$. Underlying this graph is a $2n$-dimensional vector space $V$ over a field ${\mathbb F}_q$ of odd order $q$, together with a symplectic (i.e. nondegenerate alternating…
Graph is an abstract representation commonly used to model networked systems and structure. In problems across various fields, including computer vision and pattern recognition, and neuroscience, graphs are often brought into comparison (a…
An ordered and oriented 2-component link L in the 3-sphere is said to be achiral if it is ambient isotopic to its mirror image ignoring the orientation and ordering of the components. Kirk-Livingston showed that if L is achiral then the…
Deleting a hyperplane from a polar space associated with a symplectic polarity we get a specific, symplectic, affine polar space. Similar geometry, called an \afsempol\ arises as a result of generalization of the notion of an alternating…
{Let ${\Cal X}$ be a self-dual P-polynomial association scheme. Then there are at most 12 diagonal matrices $T$ such that $(PT)^3=I$. Moreover, all of the solutions for the classical infinite families of such schemes (including the Hamming…
An association scheme on triples (AST) is a three-dimensional analogue of a classical association scheme. Similar to how a transitive group action produces a Schurian classical association scheme, a two-transitive group action produces an…
The 4-dimensional Sklyanin algebra is the homogeneous coordinate ring of a noncommutative analogue of projective 3-space. The degree-two component of the algebra contains a 2-dimensional subspace of central elements. The zero loci of those…
We present an algorithm enabling computation of the anisotropic redshift-space galaxy 3-point correlation function (3PCF) scaling as $N^2$, with $N$ the number of galaxies. Our previous work showed how to compute the isotropic 3PCF with…