Related papers: Remark on Laquer's theorem for circulant determina…

We solve Olga Taussky-Todd's circulant problem in the case of order 16.

In this paper, we give a refinement of a generalized Dedekind's theorem. In addition, we show that all possible values of integer group determinants of any group are also possible values of integer group determinants of its any abelian…

Let $\{a_k\}$ be a sequence of real numbers defined by an $m$th order linear homogenous recurrence relation. In this paper we obtain a determinant formula for the circulant matrix $A=circ(a_1, a_2, \cdots, a_n)$, providing a generalization…

This note provides formula for determinant and inverse of r-circulant matrices with general sequences of third order. In other words, the study combines many papers in the literature.

A generalized definition of the determinant of matrices is given, which is compatible with the usual determinant for square matrices and keeps many important properties, such as being an alternating multilinear function, keeping…

In this paper, the changes of representations of a group are used in order to describe its action as algebraic Galois group of an univariate polynomial on the roots of factors of any Lagrange resolvent. By this way, the Galois group of…

Let ${\rm C}_{4}$ be the cyclic group of order $4$. We determine all possible values of the integer group determinant of ${\rm C}_{4} \rtimes {\rm C}_{4}$.

We show that recent determinant evaluations involving Catalan numbers and generalisations thereof have most convenient explanations by combining the Lindstr\"om-Gessel-Viennot theorem on non-intersecting lattice paths with a simple…

We prove necessary optimality conditions of Euler-Lagrange type for generalized problems of the calculus of variations on time scales with a Lagrangian depending not only on the independent variable, an unknown function and its delta…

For any given finite abelian group, we give factorizations of the group determinant in the group algebra of any subgroup. The factorizations are an extension of Dedekind's theorem. The extension leads to a generalization of Dedekind's…

We determine all possible values of the integer group determinant of ${\rm C}_{2}^{4}$, where ${\rm C}_{2}$ is the cyclic group of order $2$.

For any positive integer $n$, let ${\rm C}_{n}$ be the cyclic group of order $n$. We determine all possible values of the integer group determinant of ${\rm C}_{2}^{2} \rtimes C_{4}$.

This work builds on Varchenko et al's introduction of bilinear forms for hyperplane arrangements, where the determinant of the associated matrices factorizes into simple components. While one of the determinant formula developed by…

We formulate necessary and sufficient conditions for an arbitrary discrete probability distribution to factor according to an undirected graphical model, or a log-linear model, or other more general exponential models. This result…

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 $4$.

For every group of order at most 14 we determine the values taken by its group determinant when its variables are integers.

It is shown that in a tower of coverings the regularized determinant of a generalized Laplacian converges to the $L^2$-determinant. This shows generic nontriviality of analytic torsion or regularized determinants since the…

Let $k \geq 2$ be an integer. We prove that factorization of integers into $k$ parts follows the Dirichlet distribution $\text{Dir}\left(\frac{1}{k},\ldots,\frac{1}{k}\right)$ by multidimensional contour integration, thereby generalizing…

The main goal of this paper is to provide a group theoretical generalization of the well-known Euler's totient function. This determines an interesting class of finite groups.

The Law of the Iterated Logarithm for some Markov operators, which converge exponentially to the invariant measure, is established. The operators correspond to iterated function systems which, for example, may be used to generalize the cell…