Related papers: A streamlined difference ring theory: Indefinite n…
In difference algebra, summability arises as a basic problem upon which rests the effective solution of other more elaborate problems, such as creative telescoping problems and the computation of Galois groups of difference equations. In…
The development of mathematics has been characterized by the increasing interconnectivity of seemingly separate disciplines. Such interplay has been facilitated by a massive development in formalism; category theory has provided a common…
In this paper, we introduce telescoping continued fractions to find lower bounds for the error term $r_n$ in Stirling's approximation $\displaystyle n! = \sqrt{2\pi}n^{n+1/2}e^{-n}e^{r_n}.$ This improves lower bounds given earlier by…
This work considers normalized inverse determinant sums as a tool for analyzing the performance of division algebra based space-time codes for multiple antenna wireless systems. A general union bound based code design criterion is obtained…
A new general and unified method of summation, which is both regular and consistent, is invented. It is based on the idea concerning a way of integers reordering. The resulting theory includes a number of explicit and closed form summation…
By considering a discrete tape where each cell corresponds to an integer, thus to a possible sum, a pseudo-polynomial solution can be given to subset sum problem, which is an NP-complete problem and a cornerstone application for this study,…
The Erd\H{o}s discrepancy problem, now a theorem by T. Tao, asks whether every sequence with values plus or minus one has unbounded discrepancy along all homogeneous arithmetic progressions. We establish weighted variants of this problem,…
Discrete tomography is concerned with the reconstruction of images that are defined on a discrete set of lattice points from their projections in several directions. The range of values that can be assigned to each lattice point is…
We reconsider the classical problem of representing a finite number of forms of degree d in n+1 variables as sums of powers of linear forms. We define a geometric construct called a `grove', which, in a number of cases allows us to…
The purpose of this paper is to provide a new account of multiplicity for finite morphisms between smooth projective varieties. Traditionally, this has been defined using commutative algebra in terms of the length of integral ring…
The theory uses methods and language of linear algebra to study nonlinear spaces. These techniques can be used particularly to describe analytic geometry of non-linear elliptic, hyperbolic, De Sitter and Anti de Sitter spaces. The main…
We show that there is the same number of (n,l)-alternating sign trapezoids as there is of column strict shifted plane partitions of class l-1 with at most n parts in the top row, thereby proving a result that was conjectured independently…
An improved multi-summation approach is introduced and discussed that enables one to simultaneously handle indefinite nested sums and products in the setting of difference rings and holonomic sequences. Relevant mathematics is reviewed and…
A method for encoding and decoding spectrum shaped binary run-length constrained sequences is described. The binary sequences with predefined range of exponential sums are introduced. On the base of Cover's enumerative scheme, recurrence…
The Numerical Assembly Technique is extended to investigate arbitrary planar frame structures with the focus on the computation of natural frequencies. This allows us to obtain highly accurate results without resorting to spatial…
We propose the method for obtaining invariants of arbitrary representations of Lie groups that reduces this problem to known problems of linear algebra. The basis of this method is the idea of a special extension of the representation…
We propose a special computational device which uses light rays for solving the subset-sum problem. The device has a graph-like representation and the light is traversing it by following the routes given by the connections between nodes.…
Nested parentheses are forms in an algebra which define orders of evaluations. A class of well-formed sets of associated opening and closing parentheses is well studied in conjunction with Dyck paths and Catalan numbers. Nested parentheses…
Similarly to how the classical group ring isomorphism problem asks, for a commutative ring $R$, which information about a finite group $G$ is encoded in the group ring $RG$, the twisted group ring isomorphism problem asks which information…
Computing the crossing number of a graph is one of the most classical problems in computational geometry. Both it and numerous variations of the problem have been studied, and overcoming their frequent computational difficulty is an active…