Symmetric and generating functions of generalized (p,q)-numbers

Generating Functions of the Incomplete Generalized Fibonacci and Generalized Lucas Numbers

Generalized symmetric functions

It is well known that over an infinite field the ring of symmetric functions in a finite number of variables is isomorphic to the one of polynomial functions on matrices that are invariants by the action of conjugation by general linear group. We generalize this result showing that the abelianization of the algebra of the symmetric tensors of fixed order over a free associative algebra is isomo...

Lattice Point Generating Functions and Symmetric Cones

Abstract. We show that a recent identity of Beck–Gessel–Lee–Savage on the generating function of symmetrically contrained compositions of integers generalizes naturally to a family of convex polyhedral cones that are invariant under the action of a finite reflection group. We obtain general expressions for the multivariate generating functions of such cones, and work out their general form more...

On composition of generating functions

In this work we study numbers and polynomials generated by two type of composition of generating functions and get their explicit formulae. Furthermore we state an improvementof the composita formulae's given in [6] and [3], using the new composita formula's we construct a variety of combinatorics identities. This study go alone to dene new family of generalized Bernoulli polynomials which incl...

Generating functions and companion symmetric linear functionals

In this contribution we analyze the generating functions for polynomials orthogonal with respect to a symmetric linear functional u, i.e., a linear application in the linear space of polynomials with complex coefficients such that u(x) = 0. In some cases we can deduce explicitly the expression for the generating function P(x,ω) = ∞ ∑