Extension of the Bernoulli and Eulerian Polynomials of Higher Order and Vector Partition Function

Original · EN

Following the ideas of L. Carlitz we introduce a generalization of the Bernoulli and Eulerian polynomials of higher order to vectorial index and argument. These polynomials are used for computation of the vector partition function W(s, D), i.e., a number of integer solutions to a linear system x ≥ 0, D x = s. It is shown that W(s, D) can be expressed through the vector Bernoulli polynomials of higher order.