Related papers: Christoffel Matrices and Sturmian Determinants
We determine all possible values of the integer group determinant of ${\rm C}_{4}^{2}$, where ${\rm C}_{4}$ is the cyclic group of order $4$.
We exhibit explicit expressions, in terms of components, of discriminants, determinants, characteristic polynomials and polynomial identities for matrices of higher rank. We define permutation tensors and in term of them we construct…
We present explicit formulas for a set of generators of the ideal of relations among the pfaffians of the principal minors of the antisymmetric matrices of fixed dimension. These formulas have an interpretation in terms of the standard…
We study the dependence of a cluster algebra on the choice of coefficients. We write general formulas expressing the cluster variables in any cluster algebra in terms of the initial data; these formulas involve a family of polynomials…
Bleher and Kuijlaars recently showed that the eigenvalue correlations from matrix ensembles with external source can be expressed by means of a kernel built out of special multiple orthogonal polynomials. We derive a Christoffel-Darboux…
A balanced word is one in which any two factors of the same length contain the same number of each letter of the alphabet up to one. Finite binary balanced words are called Sturmian words. A Sturmian word is bispecial if it can be extended…
In this article we build a Quillen model category structure on the category of sequentially complete l.m.c.-C*-algebras such that the corresponding homotopy classes of maps Ho(A,B) for separable C*-algebras A and B coincide with the…
We present a new, dynamical way to study powers (that is, repetitions) in Sturmian words based on results from Diophantine approximation theory. As a result, we provide an alternative and shorter proof of a result by Damanik and Lenz…
It is proposed to use the Lie group theory of symmetries of differential equations to investigate the system of equations describing a static star in a radiative and convective equilibrium. It is shown that the action of an admissible group…
Representations of the Schlessinger-Stasheff's associative homotopy Lie algebras in the spaces of higher-order differential operators are analyzed; in particular, a remarkable identity for the Wronskian determinants is obtained. The…
A finite Sturmian word w over the alphabet {a,b} is left special (resp. right special) if aw and bw (resp. wa and wb) are both Sturmian words. A bispecial Sturmian word is a Sturmian word that is both left and right special. We show as a…
We describe the Gerstenhaber bracket structure on Hochschild cohomology of Koszul quiver algebras in terms of homotopy lifting maps. There is a projective bimodule resolution of Koszul quiver algebras that admits a comultiplicative…
We define quantum determinants in Quantum Matrix Algebras, related to couples of compatible braidings following the scheme from [G]. We establish relations between these determinants and the so-called column-(row-)determinants, often used…
We introduce the notion of Lusternik-Schnirelmann category for differentiable stacks and establish its relation with the groupoid Lusternik-Schnirelmann category for Lie groupoids.
The Shapovalov determinant for a class of pointed Hopf algebras is calculated, including quantized enveloping algebras, Lusztig's small quantum groups, and quantized Lie superalgebras. Our main tools are root systems, Weyl groupoids, and…
We illustrate the potential applications in machine learning of the Christoffel function, or more precisely, its empirical counterpart associated with a counting measure uniformly supported on a finite set of points. Firstly, we provide a…
We derive a formula connecting the orders of the automorphism groups of a finite group and of its covering groups.
Ziv-Lempel and Crochemore factorization are two kinds of factorizations of words related to text processing. In this paper, we find these factorizations for standard epiesturmian words. Thus the previously known c-factorization of standard…
In this paper we consider pentadiagonal $(n+1)\times(n+1)$ matrices with two subdiagonals and two superdiagonals at distances $k$ and $2k$ from the main diagonal where $1\le k<2k\le n$. We give an explicit formula for their determinants and…
Operators acting on the discrete random chaos yield signed multiplicative systems, extending the notion of spin matrices and quaternions. We investigate signed groups through the associated sign matrices, focusing on generators and their…