Related papers: Minor Identities for Quasideterminants and Quantum…
We clarify the algebraic structure of continuous and discrete quasi-exactly solvable spectral problems by embedding them into the framework of the quantum inverse scattering method. The quasi-exactly solvable hamiltonians in one dimension…
Matrix-product codes over finite fields are an important class of long linear codes by combining several commensurate shorter linear codes with a defining matrix over finite fields. The construction of matrix-product codes with certain…
In the context of generating uniform random contingency tables with pre-specified marginals, the number of (binary) matrices with given row- and column-sums is a well-studied object in the literature. We will denote this number by $N(p,q)$,…
Some generalized multi-sum Chu-Vandermonde identities are presented and proved, generalizing some known multi-sum Chu-Vandermonde identities from literature and adding some quadratic and cubic examples of these identities. Some other…
There are quantum circuit identities that simplify quantum circuits, reducing the effort needed physically to implement them. This paper constructs all identities made from 3 or fewer operations taken from a common set of one qubit…
Formalism of differential forms is developed for a variety of Quantum and noncommutative situations.
In this paper we give new identities involving q-Euler polynomials of higher order.
We consider the characterizations of positive definite as well as nonnegative definite quadratic forms in terms of the principal minors of the associated symmetric matrix. We briefly review some of the known proofs, including a classical…
For positive integers $n,n'$, we give a combinatorial characterization for the set of quadratic inequalities on minors that are valid for all $n\times n'$ totally nonnegative matrices. This is obtained as a consequence from our earlier…
Using the quantum cluster algebra formalism of Fock and Goncharov, we present several forms of quantum dilogarithm identities associated with periodicities in quantum cluster algebras, namely, the tropical, universal, and local forms. We…
In this article we derive a useful expectation identity using the language of quantum statistical mechanics, where density matrices represent the state of knowledge about the system. This identity allows to establish relations between…
Almost strictly sign regular matrices are sign regular matrices with a special zero pattern and whose nontrivial minors are nonzero. In this paper we provide several properties of almost strictly sign regular rectangular matrices and…
We establish new product identities involving the $q$-analogue of the Fibonacci numbers. We show that the identities lead to alternate expressions of generating functions for close-packed dimers on non-orientable surfaces.
By using the quasi-determinant the construction of Gel'fand et al. leads to the inverse of a matrix with noncommuting entries. In this work we offer a new method that is more suitable for physical purposes and motivated by deformation…
Quasi-set theory is a first order theory without identity, which allows us to cope with non-individuals in a sense. A weaker equivalence relation called ``indistinguishability'' is an extension of identity in the sense that if $x$ is…
We develop explicit formulae for the eigenvalues of various invariants for highest weight irreducible representations of the quantum supergroup $U_q[gl(m|n)]$. The techniques employed make use of modified characteristic identity methods and…
We give generalizations of a finite version of Euler's pentagonal number theorem and of a q-identity of Gauss.
We define and study q-delta-matroids, and q-g-matroids. These objects are analogues, for finite-dimensional vector spaces over finite fields, of delta-matroids and g-matroids arising from finite sets. We compare axiomatic descriptions with…
The q-generalizations of the two fundamental statements of matrix algebra -- the Cayley-Hamilton theorem and the Newton relations -- to the cases of quantum matrix algebras of an "RTT-" and of a "Reflection equation" types have been…
The purpose of this article is to give a short introduction to the concept of quasi-unitary equivalence of quadratic forms and its consequences. In particular, we improve an estimate concerning the transitivity of quasi-unitary equivalence…