Related papers: Congruence invariants of matrix mutation

We study numerical computation of several conformal invariants of simply connected domains in the complex plane including, the hyperbolic distance, the reduced modulus, the harmonic measure, and the modulus of a quadrilateral. The method we…

We present necessary and sufficient conditions for an n\times n complex matrix B to be unitarily similar to a fixed unicellular (i.e., indecomposable by similarity) n\times n complex matrix A

We find and prove a class of congruences modulo 4 for Andrews' partition with certain ternary quadratic form. We also discuss distribution of $\overline{\mathcal{EO}}(n)$ and further prove that $\overline{\mathcal{EO}}(n)\equiv0\pmod4$ for…

We study spaces of matrices coming from irreducible representations of reductive groups over an algebraically closed field of characteristic zero and we completely classify those of constant corank one. In particular, we recover the…

We provide new examples of integrable rational maps in four dimensions with two rational invariants, which have unexpected geometric properties, as for example orbits confined to non algebraic varieties, and fall outside classes studied by…

We study a class of matrices with noncommutative entries, which were first considered by Yu. I. Manin in 1988 in relation with quantum group theory. They are defined as "noncommutative endomorphisms" of a polynomial algebra. More explicitly…

Noncommutative invariant theory is a generalization of the classical invariant theory of the action of $SL(2,\IC)$ on binary forms. The dimensions of the spaces of invariant noncommutative polynomials coincide with the numbers of certain…

This paper presents a comprehensive description of the coordinate rings and Poisson brackets associated with the fourth Calogero-Moser space and invariant commuting pairs of matrices of size four. As an application, we compute their…

The goal of this paper is a classification theorem of the singularities according to a new invariant, Mather discrepancy. On the other hand, we show some evidences convincing us that Mather discrepancy is a considerable invariant: By…

L.Huang [Linear Algebra Appl. 331 (2001) 21-30] gave a canonical form of a quaternion matrix $A$ with respect to consimilarity transformations $\tilde{S}^{-1}AS$ in which $S$ is a nonsingular quaternion matrix and $\tilde{h}:=a-bi+cj-dk$…

This paper identifies a new class of shape invariant models. These models are based on extensions of conventional quantum mechanics that satisfy a string-motivated minimal length uncertainty relation. An important feature of our…

The modular data of a modular category $\mathcal{C}$, consisting of the $S$-matrix and the $T$-matrix, is known to be an incomplete invariant of $\mathcal{C}$. More generally, the invariants of framed links and knots defined by a modular…

Model sets (also called cut and project sets) are generalizations of lattices, and multi-component model sets are generalizations of lattices with colourings. In this paper, we study self-similarities of multi-component model sets. The main…

This paper presents a framework based on matrices of monoids for the study of coupled cell networks. We formally prove within the proposed framework, that the set of results about invariant synchrony patterns for unweighted networks also…

In these notes we focus a bit on the complex case for some families of matrices and equivalences between them.

The problem of normalisation of the modular forms in modular invariant lepton and quark flavour models is discussed. Modular invariant normalisations of the modular forms are proposed.

Finite dimensional modular Lie superalgebras over algebraically closed fields with indecomposable Cartan matrices are classified under some technical, most probably inessential, hypotheses. If the Cartan matrix is invertible, the…

We introduce a notion of retraction between continuous maps of topological spaces and study the behavior of several numerical invariants under such retractions. These include (co)homological dimensions, the Lusternik-Schnirelmann category,…

Recently, Andrews, Hirschhorn and Sellers have proven congruences modulo 3 for four types of partitions using elementary series manipulations. In this paper, we generalize their congruences using arithmetic properties of certain quadratic…

Let X be a smooth complex variety and Y be a closed subvariety of X, or more generally, a closed subscheme of X. We are interested in invariants attached to the singularities of the pair (X, Y). We discuss various methods to construct such…