Related papers: Generating-function method for tensor products
Many modern data sets are sampled with error from complex high-dimensional surfaces. Methods such as tensor product splines or Gaussian processes are effective/well suited for characterizing a surface in two or three dimensions but may…
To compute difference Groebner bases of ideals generated by linear polynomials we adopt to difference polynomial rings the involutive algorithm based on Janet-like division. The algorithm has been implemented in Maple in the form of the…
The deep theory of approximate subgroups establishes 3-step product growth for subsets of finite simple groups $G$ of Lie type of bounded rank. In this paper we obtain 2-step growth results for representations of such groups $G$ (including…
The powers of generating functions and its properties are analyzed. A new class of functions is introduced, based on the application of compositions of an integer $n$, called composita. The methods for obtaining reciprocal and reverse…
A recursive method is given for finding generating functions which enumerate rooted hypermaps by number of vertices, edges and faces for any given number of darts. It makes use of matrix-integral expressions arising from the study of…
The method of direct computation of universal (fibred) product in the category of commutative associative algebras of finite type with unity over a field is given and proven. The field of coefficients is not supposed to be algebraically…
Since their introduction by Andrews, generalized Frobenius partitions have interested a number of authors, many of whom have worked out explicit formulas for their generating functions in specific cases. This has uncovered interesting…
Originally motivated by questions of P. Etingof related to growth rates of tensor powers in symmetric tensor categories, we obtain general bounds on the order of finite subgroups of ${\rm GL}(n,\mathbb{C})$ with restricted composition…
We show how the combined use of the generating function method and of the theory of multivariable Hermite polynomials is naturally suited to evaluate integrals of gaussian functions and of multiple products of Hermite polynomials.
The tensor-tensor product (t-product) [M. E. Kilmer and C. D. Martin, 2011] is a natural generalization of matrix multiplication. Based on t-product, many operations on matrix can be extended to tensor cases, including tensor SVD, tensor…
Let $L_n(k)$ denote the least common multiple of $k$ independent random integers uniformly chosen in $\{1,2,\ldots ,n\}$. In this note, using a purely probabilistic approach, we derive a criterion for the convergence in distribution as…
We describe a general approach to obtain the generating functions of the characters of simple Lie algebras which is based on the theory of the quantum trigonometric Calogero-Sutherland model. We show how the method works in practice by…
Fusion product originates in the algebraisation of the operator product expansion in conformal field theory. Read and Saleur (2007) introduced an analogue of fusion for modules over associative algebras, for example those appearing in the…
Using the notion of multivariate lower set interpolation, we construct nodal basis functions for the serendipity family of finite elements, of any order and any dimension. For the purpose of computation, we also show how to express these…
We construct the tensor product for f-algebras, including proving a universal property for it, and investigate how it preserves algebraic properties of the factors.
The generating series of a number of different objects studied in arithmetic statistics can be built out of Euler products. Euler products often have very nice analytic properties, and by constructing a meromorphic continuation one can use…
The main aim of this paper is to provide a unified approach to deriving identities for the Bernstein polynomials using a novel generating function. We derive various functional equations and differential equations using this generating…
We present an effective algorithm for computing the standard cohomology spaces of finitely generated Lie (super) algebras over a commutative field K of characteristic zero. In order to reach explicit representatives of some generators of…
The joint use of counting functions, Hilbert basis and Markov basis allows to define a procedure to generate all the fractions that satisfy a given set of constraints in terms of orthogonality. The general case of mixed level designs,…
A convenient technique for calculating completed topological tensor products of functional Frechet and DF spaces is developed. The general construction is applied to proving kernel theorems for a wide class of spaces of smooth and entire…