Related papers: On the binomial interpolated triangles
Transformations in the field of computer graphics and geometry are one of the most important concepts for efficient manipulation and control of objects in 2-dimensional and 3-dimensional space. Transformations take many forms each with…
Many sequences of binomial coefficients share various unimodality properties. In this paper we consider the unimodality problem of a sequence of binomial coefficients located in a ray or a transversal of the Pascal triangle. Our results…
We study the interpolation group whose elements are suitable pairs of formal power series. This group has a faithful representation into infinite lower triangular matrices and carries thus a natural structure as a Lie group. The matrix…
There are several examples of spaces of univariate functions for which we have a characterization of all sets of knots which are poised for the interpolation problem. For the standard spaces of univariate polynomials, or spline functions…
In this short note, we merge the areas of hypercomplex algebras with that of fractal interpolation and approximation. The outcome is a new holistic methodology that allows the modelling of phenomena exhibiting a complex self-referential…
We introduce a generalization of Pascal triangle based on binomial coefficients of finite words. These coefficients count the number of times a word appears as a subsequence of another finite word. Similarly to the Sierpi\'nski gasket that…
Here the polynomial interpolation approach is used to introduce the main results on multivariate normal algebraic systems. Next we bring a construction which shows that any standard algebraic system, with finite set of solutions, can be…
This article focuses on trigonometric Riemann B-splines and Riemann kernels of trigonometric interpolation splines of arbitrary order; it is shown that trigonometric interpolation splines are a convolution of trigonometric B-splines with…
We study the Hankel transforms of sequences related to the central coefficients of a family of Pascal-like triangles. The mechanism of Riordan arrays is used to elucidate the structure of these transforms.
This work is divided into three parts. The first part concerns polynomials in one variable with all real roots. We consider linear transformations that preserve real rootedness, as well as matrices that preserve interlacing. The second part…
This paper is devoted to the study of eigen-sequences for some important operators acting on sequences. Using functional equations involving generating functions, we completely solve the problem of characterizing the fixed sequences for the…
Provided a special function of one variable and some of its derivatives can be accurately computed over a finite range, a method is presented to build a series of polynomial approximations of the function with a defined relative error over…
The classic way to write down Pascal's triangle leads to entries in alternating rows being vertically aligned. In this paper, we prove a linear dependence on vertically aligned entries in Pascal's triangle. Furthermore, we give an…
Many polynomial invariants are defined on graphs for encoding the combinatorial information and researching them algebraically. In this paper, we introduce the cycle polynomial and the path polynomial of directed graphs for counting cycles…
In this study, we apply "r" times the binomial transform to the Padovan and Perrin matrix sequences. Also, the Binet formulas, summations, generating functions of these transforms are found using recurrence relations. Finally, we give the…
This paper applies a complete parametric set for approximating the geometry of a quadrilateral element. The approximation basis used is a complete Pascal polynomial of second order with six free parameters. The interpolation procedure is a…
We give a simplified presentation of some results about recurrences of certain sequences of binomial sums in terms of (generalized) Fibonacci and Lucas polynomials.
In this paper, we introduce some difference sequence spaces in bigeometric calculus. We determine the $\alpha$-duals of these sequence spaces and study their matrix transformations. We also develop an interpolating polynomial in bigeometric…
With every family of finitely many subsets of a finite-dimensional vector space over the Galois-field with two elements we associate a cyclic transversal polytope. It turns out that those polytopes generalize several well-known polytopes…
We study a one-parameter family of binomial-convolution operators acting on sequences. These operators form an additive semigroup with an explicit inverse, and they subsume iterated classical binomial transforms as a special case. We…