Related papers: A generating operator for Rankin-Cohen brackets
We present a new method to obtain the generating functions for directed convex polyominoes according to several different statistics including: width, height, size of last column/row and number of corners. This method can be used to study…
We introduce two q-analogues of the 2D-Hermite polynomials which are functions of two complex variables. We derive explicit formulas, orthogonality relations, raising and lowering operator relations, generating functions, and Rodrigues…
We find an explicit expression for the generating function of the number of permutations in S_n avoiding a subgroup of S_k generated by all but one simple transpositions. The generating function turns out to be rational, and its denominator…
We present an approach for construction of functional bases of differential invariants for some infinite-dimensional algebras with coefficients of generating operators depending on arbitrary functions. An example for the…
In 1954, Atkin and Swinnerton-Dyer proved Dyson's conjectures on the rank of a partition by establishing formulas for the generating functions for rank differences in arithmetic progressions. In this paper, we prove formulas for the…
In this notes it will be provided a set of techniques which can help one to understand the proof of the Hochschild-Kostant-Rosenberg theorem for differentiable manifolds. Precise definitions of multidiferential operators and polyderivations…
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…
We present an overview of the role of generating functions in quantum mechanical contexts, mainly in the modern theory of polarization and in the study of quantum phase transitions. Generating functions enable the derivation of moments and…
We derive generating functions for the ranks of pre-modular categories associated to quantum groups at roots of unity.
We give the generating function for the index of integer lattice points, relative to a finite order ideal. The index is an important concept in the theory of border bases, an alternative to Gr\"obner bases. Equivalently, we explicitly solve…
Clifford geometric algebras of multivectors are treated in detail. These algebras are build over a graded space and exhibit a grading or multivector structure. The careful study of the endomorphisms of this space makes it clear, that…
An algorithm is given for computing explicit formulas for the generators of relations among the invariant rational functions for vector-valued bilinear forms. These formulas have applications in the geometry of Riemannian submanifolds and…
Based on the Lie theoretical methods of algebraic Fourier transformation, we classify in the case of generic values of inducing parameters the scalar singular vectors corresponding to the diagonal branching rules for scalar generalized…
We describe generating functions for several important families of classical symmetric functions and shifted Schur functions. The approach is originated from vertex operator realization of symmetric functions and offers a unified method to…
In the context of Higman embeddings of recursive groups into finitely presented groups we suggest an algorithm which uses Higman operations to explicitly constructs the specific recursively enumerable sets of integer sequences arising…
We study orthogonal polynomials for a weight function defined over a domain of revolution, where the domain is formed from rotating a two-dimensional region and goes beyond the quadratic domains. Explicit constructions of orthogonal bases…
We establish new operational formulae of Burchnall type for the complex disk polynomials (generalized Zernike polynomials). We then use them to derive some interesting identities involving these polynomials. In particular, we establish…
In this paper, by making use of the familiar $q$-difference operators $D_q$ and $D_{q^{-1}}$, we first introduce two homogeneous $q$-difference operators $\mathbb{T}({\bf a},{\bf b},cD_q)$ and $\mathbb{E}({\bf a},{\bf b}, cD_{q^{-1}})$,…
Utilization of classification latent space information for downstream reconstruction and generation is an intriguing and a relatively unexplored area. In general, discriminative representations are rich in class-specific features but are…
We use the method of similar operators to study a mixed problem for a differential equation with an involution and an operator-valued potential function. The differential operator defined by the equation is transformed into a similar…