Related papers: Compounding Doubly Affine Matrices
We calculate the cluster modular groups of affine and doubly extended typecluster algebras in a uniform way by introducing a new family of quivers. We use this uniformdescription to construct a natural finite quotient of the cluster complex…
We propose '$\mathrm{d} \mathcal{E}$-forms' as fundamental building blocks of canonical integrands for elliptic Feynman integrals, which lead to Kronecker-Eisenstein $\omega$-form symbol letters. Built upon pure elliptic multiple…
Two harmonic extraction based Jacobi--Davidson (JD) type algorithms are proposed to compute a partial generalized singular value decomposition (GSVD) of a large regular matrix pair. They are called cross product-free (CPF) and inverse-free…
Let $(\Gamma,+)$ be an Abelian group of order $n^2$. A $\Gamma$-magic square of order $n$ is an $n\times n$ array whose entries are pairwise distinct elements of $\Gamma$ such that all row sums, column sums, and the two main diagonal sums…
In this paper a two-sided, parallel Kogbetliantz-type algorithm for the hyperbolic singular value decomposition (HSVD) of real and complex square matrices is developed, with a single assumption that the input matrix, of order $n$, admits…
There is often a significant trade-off between formulation strength and size in mixed integer programming (MIP). When modeling convex disjunctive constraints (e.g. unions of convex sets), adding auxiliary continuous variables can sometimes…
We study the properties of singular values of mixing matrices embedded within an experimentally determined interval matrix. We argue that any physically admissible mixing matrix needs to have the property of being a contraction. This…
Magic squares are well-known arrangements of integers with common row, column, and diagonal sums. Various other magic shapes have been proposed, but triangles have been somewhat overlooked. We introduce certain triangular arrangements of…
Highlighting the use of critical classes, we consider constituents in Kronecker products, in particular of spin characters of the double covers of the symmetric and alternating groups. We apply results from the spin case to find…
When two boundary-parabolic representations of knot groups are given, we introduce the connected sum of these representations and show several natural properties including the unique factorization property. Furthermore, the complex volume…
We introduce the notion of polynomial-depth duality transformations, which relates two sets of operator algebras through a conjugation by a poly-depth quantum circuit, and make use of this to construct efficient Gibbs samplers for a variety…
A new family of polynomials, called cumulant polynomial sequence, and its extensions to the multivariate case is introduced relied on a purely symbolic combinatorial method. The coefficients of these polynomials are cumulants, but depending…
Many eigenvalue matrix models possess a peculiar basis of observables which have explicitly calculable averages. This explicit calculability is a stronger feature than ordinary integrability, just like the cases of quadratic and Coulomb…
Linear least-squares regression with a "design" matrix A approximates a given matrix B via minimization of the spectral- or Frobenius-norm discrepancy ||AX-B|| over every conformingly sized matrix X. Another popular approximation is…
If $A$ is an $n\times n$ matrix whose $n$ eigenvalues are ordered in terms of decreasing modules, $|\lambda_1 | \geq |\lambda_2| \geq ... |\lambda_n|$, it is often of interest to estimate $\frac{|\lambda_2|}{|\lambda_1|}$. If $A$ is a row…
Dual complex numbers can represent rigid body motion in 2D spaces. Dual complex matrices are linked with screw theory, and have potential applications in various areas. In this paper, we study low rank approximation of dual complex…
Cosine similarity is widely used to measure the similarity between two embeddings, while interpretations based on angle and correlation coefficient are common. In this study, we focus on the interpretable axes of embeddings transformed by…
The starting point for this work is an identity that relates the number of minimal matrices with prescribed 1-marginals and coefficient sequence to a linear combination of Kronecker coefficients. In this paper we provide a bijection that…
We demonstrate the existence of $K$-multimagic squares of order $N$ consisting of distinct integers whenever $N>2 K(K+1)$. This improves upon our earlier result in which we only required $N+1$ distinct integers. Additionally, we present a…
Orthogonal array and a large set of orthogonal arrays are important research objects in combinatorial design theory, and they are widely applied to statistics, computer science, coding theory and cryptography. In this paper, some new series…