Related papers: A binary invariant of matrix mutation

We consider the 2-generated free metabelian associative and Lie algebras over the complex field and the invariants of the dihedral groups of finite order acting on these algebras. In the associative case we find a finite set of generators…

We construct a bar involution for quantum symmetric pair coideal subalgebras $B_{\mathbf{c},\mathbf{s}}$ corresponding to involutive automorphisms of the second kind of symmetrizable Kac-Moody algebras. To this end we give unified…

Let $V$ be a nonempty finite set and $A=(a_{ij})_{i,j\in V}$ be a matrix with entries in a field $\mathbb{K}$. For a subset $X$ of $V$, we denote by $A[X]$ the submatrix of $A$ having row and column indices in $X$. We study the following…

We introduce a new class of problems lying halfway between questions about graph capacity and intersection. We say that two binary sequences x and y of the same length have a skewincidence if there is a coordinate i for which x_i=y_{i+1}=1…

We classify small binary bibraces, using the correspondence with alternating algebras over the field F2, up to dimension eight, also determining their isomorphism classes. These finite-dimensional algebras, defined by an alternating…

We prove a conjecture of Crapo and Penne which characterizes isotopy classes of skew configurations with spindle-structure. We use this result in order to define an invariant, spindle-genus, for spindle-configurations. We also slightly…

Using evaluation at appropriately chosen points, we propose a Gr\"obner basis free approach for calculating the secondary invariants of a finite permutation group. This approach allows for exploiting the symmetries to confine the…

This article gives a new matrix function named "twisted immanant," which can be regarded as an analogue of the immanant. This is defined for each self-conjugate partition through a "twisted" analogue of the irreducible character of the…

We present the weighted weak group inverse, which is a new generalized inverse of operators between two Hilbert spaces, introduced to extend weak group inverse for square matrices. Some characterizations and representations of the weighted…

We describe differential invariants of infinite-dimensional algebras being equivalence algebras of some classes of PDE and study structure of these algebras.

For a finite dimensional hereditary algebra, we consider: exceptional sequences in the category of finite dimensional modules, silting objects in the bounded derived category, and m-cluster tilting objects in the m-cluster category. There…

The theory of Topological Modular Forms suggests the existence of deformation invariants for two-dimensional supersymmetric field theories that are more refined than the standard elliptic genus. In this note we give a physical definition of…

We use weighted unfoldings of quivers to provide a categorification of mutations of quivers of types $I_2(2n)$, thus extending the construction of categorifications of mutations of quivers to all finite types.

We construct new invariants of equivariant birational isomorphisms taking values in equivariant Burnside groups.

A cluster algebra is a commutative algebra whose structure is decided by a skew-symmetrizable matrix or a quiver. When a skew-symmetrizable matrix is invariant under an action of a finite group and this action is admissible, the folded…

We introduce the notion of a combinatorial inverse system in non-commutative variables. We present two important examples, some conjectures and results. These conjectures and results were suggested and supported by computer investigations.

We introduce a Sinkhorn-type algorithm for producing quantum permutation matrices encoding symmetries of graphs. Our algorithm generates square matrices whose entries are orthogonal projections onto one-dimensional subspaces satisfying a…

Permutation Matrices are a well known class of matrices which encode the elements of the symmetric group on $d$ elements as a square $d\times d$ matrix. Motivated by [4], we define a similar class of matrices which are a generalization of…

In this paper we extend a so called frame-like formulation of massless high spin particles to massive case. We start with two explicit examples of massive spin 2 and spin 3 particles and then construct gauge invariant description for…

In this note, we give an exposition of the construction of Seiberg-Witten invariants.