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

## Published Web Location

https://arxiv.org/pdf/math/0612076.pdfNo data is associated with this publication.

## Abstract

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 $W({\bf s},{\bf D})$, i.e., a number of integer solutions to a linear system ${\bf x} \ge 0, {\bf D x} = {\bf s}$. It is shown that $W({\bf s},{\bf D})$ can be expressed through the vector Bernoulli polynomials of higher order.