Related papers: Convolution numbers: the cyclic case
We introduce a shifted version of the binomial theorem, and use it to study some remarkable trigonometric integrals and their explicit rewriting in terms of binomial multiple sums. Motivated by the expressions of area generating functions…
We investigate compositions of a positive integer with a fixed number of parts, when there are several types of each natural number. These compositions produce new relationships among binomial coefficients, Catalan numbers, and numbers of…
We perform a non-perturbative sum over geometries in a (2+1)-dimensional quantum gravity model given in terms of Causal Dynamical Triangulations. Inspired by the concept of triangulations of product type introduced previously, we impose an…
We introduce the three-Catalan triangle, highlighting the three-Catalan numbers along with their recurrence relation and combinatorial interpretation, which allows us to establish their log-convexity. Additionally, we prove that the rows of…
Codes from generalized Hadamard matrices have already been introduced. Here we deal with these codes when the generalized Hadamard matrices are cocyclic. As a consequence, a new class of codes that we call generalized Hadamard full…
We study the theory of systems with constraints from the point of view of the formal theory of partial differential equations. For finite-dimensional systems we show that the Dirac algorithm completes the equations of motion to an…
A notion of convolution is presented in the context of formal power series together with lifting constructions characterising algebras of such series, which usually are quantales. A number of examples underpin the universality of these…
We propose a flexible family of distributions, generalized $t$-distributions, on the cylinder which is obtained as a conditional distribution of a trivariate $t$ distribution. The new distribution has unimodality or bimodality, symmetry or…
Variable-exponent fractional models attract increasing attentions in various applications, while the rigorous analysis is far from well developed. This work provides general tools to address these models. Specifically, we first develop a…
By using the Newton interpolation formula, we generalize the recent identities on the Catalan triangle obtained by Miana and Romero as well as those of Chen and Chu. We further study divisibility properties of sums of products of binomial…
We introduce several classes of polytopes contained in $[0,1]^n$ and cut out by inequalities involving sums of consecutive coordinates. We show that the normalized volumes of these polytopes enumerate circular extensions of certain partial…
This paper studies a family of convolution quadratures, a numerical technique for efficient evaluation of convolution integrals. We employ the block generalized Adams method to discretize the underlying initial value problem, departing from…
We provide a generalization and new proofs of the formulas of Collins, Hasebe and Sakuma for the spectrum of polynomials in cyclic monotone elements. This is applied to random matrices with discrete spectrum.
A new generalized cyclic symmetric structure in the factor matrices of polyadic decompositions of matrix multiplication tensors for non-square matrix multiplication is proposed to reduce the number of variables in the optimization problem…
We obtain a series transformation formula involving the classical Hermite polynomials. We then provide a number of applications using appropriate binomial transformations. Several of the new series involve Hermite polynomials and harmonic…
In this paper, we study convolutional codes with a specific cyclic structure. By definition, these codes are left ideals in a certain skew polynomial ring. Using that the skew polynomial ring is isomorphic to a matrix ring we can describe…
We recognise Harada's generalized categories of diagrams as a particular case of modules over a monad defined on a finite direct product of additive categories. We work in the dual (albeit formally equivalent) situation, that is, with…
This paper deals with the regularization of the sum of functions defined on a locally convex spaces through their closed-convex hulls in the bidual space. Different conditions guaranteeing that the closed-convex hull of the sum is the sum…
We study the decomposition of real numbers into sums of L\"uroth sets, which are defined by numbers whose L\"uroth expansions have prescribed digit constraints. We establish several results on the congruence modulo 1 of sums of L\"uroth…
The determination of weight distribution of cyclic codes involves evaluation of Gauss sums and exponential sums. Despite of some cases where a neat expression is available, the computation is generally rather complicated. In this note, we…