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

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

2006-12-04

arxiv.org/abs/math/0612076v1

Mathematics

Combinatorics

18 pages

Scientific paper

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.

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