Related papers: Totally bipartite tridiagonal pairs

We define genuine total, classical and quantum correlations in tripartite systems. The measure we propose is based on the idea that genuine tripartite correlation exists if and only if the correlation between any bipartition does not…

Let $K$ denote a field and let $V$ denote a vector space over $K$ with finite positive dimension. By definition a Leonard pair on $V$ is a pair of linear transformations $A:V\to V$ and $A^*:V\to V$ that satisfy the following two conditions:…

Motivated by the concept of well-covered graphs, we define a graph to be well-bicovered if every vertex-maximal bipartite subgraph has the same order (which we call the bipartite number). We first give examples of them, compare them with…

A digraph is semicomplete multipartite if its underlying graph is a complete multipartite graph. As a special case of semicomplete multipartite digraphs, J{\o}rgensen et al. \cite{JG14} initiated the study of doubly regular team…

Isotopic pairs and their representations are considered in a general framework of the vector superalgebra. Numerous examples of finite-dimensional and infinite-dimensional isotopic pairs are discussed. Several types of their representations…

The task of analytically diagonalizing a tridiagonal matrix can be considerably simplified when a part of the matrix is uniform. Such quasi-uniform matrices occur in several physical contexts, both classical and quantum, where…

Poisson superpair is a pair of Poisson superalgebra structures on a super commutative associative algebra, whose any linear combination is also a Poisson superalgebra structure. In this paper, we first construct certain linear and quadratic…

Let $K$ denote a field, and let $V$ denote a vector space over $K$ with finite positive dimension. Consider a pair of linear transformations $A:V\to V$ and $A^*:V\to V$ that satisfy both conditions below: (i) There exists a basis for $V$…

We introduce the triangulant of two matrices, and relate it to the existence of orthogonal eigenvectors. We also use it for a new characterization of mutually unbiased bases. Generalizing the notion, we introduce higher order triangulants…

The five parameter family of multivariable Askey-Wilson polynomials is studied with four parameters generically complex. The multivariable Askey-Wilson polynomials form an orthogonal system with respect to an explicit (in general complex)…

In this work, we construct a new Bailey pairs for the integral pentagon identity in terms of q-hypergeometric functions. The pentagon identity considered here represents equality of the partition functions of a certain three-dimensional…

The theory of bi-orthogonal polynomials on the unit circle is developed for a general class of weights leading to systems of recurrence relations and derivatives of the polynomials and their associated functions, and to…

We review properties of q-orthogonal polynomials, related to their orthogonality, duality and connection with the theory of symmetric (self-adjoint) operators, represented by a Jacobi matrix. In particular, we show how one can naturally…

The total matching polytope generalizes the stable set polytope and the matching polytope. In this paper, we first propose new facet-defining inequalities for the total matching polytope. We then give an exponential-sized, non-redundant…

We study the algebraic structure of the mesonic moduli spaces of bipartite field theories by computing the Hilbert series. Bipartite field theories form a large family of 4d N=1 supersymmetric gauge theories that are defined by bipartite…

Let $G$ be a tripartite graph with $N$ vertices in each vertex class. If each vertex is adjacent to at least $(2/3)N$ vertices in each of the other classes, then either $G$ contains a subgraph that consists of $N$ vertex-disjoint triangles…

Triangular algebras, and maximal triangular algebras in particular, have been objects of interest for over fifty years. Rich families of examples have been studied in the context of many w$^*$- and C$^*$-algebras, but there remains a dearth…

This paper deals with the problem of finding totally antimagic total labelings of complete bipartite graphs. We prove that complete bipartite graphs are totally antimagic total graphs. We also show that the join of complete bipartite graphs…

In this paper, the intersection of bivariate orthogonal polynomials on triangle patches will be investigated. The result is interesting by its own but also has important applications in the theory of a posteriori error estimation for finite…

For an integer $n\geq 2$, the triangular graph has vertex set the $2$-subsets of $\{1,\ldots,n\}$ and edge set the pairs of $2$-subsets intersecting at one point. Such graphs are known to be halved graphs of bipartite rectagraphs, which are…