Extension of the Bernoulli and Eulerian Polynomials of Higher Order and Vector Partition Function
نویسنده
چکیده
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, Dx = s. It is shown that W (s,D) can be expressed through the vector Bernoulli polynomials of higher order.
منابع مشابه
Restricted partition functions as Bernoulli and Eulerian polynomials of higher order
Abstract Explicit expressions for restricted partition function W (s, d) and its quasiperiodic components W j (s, dm) (called Sylvester waves) for a set of positive integers dm = {d1, d2, . . . , dm} are derived. The formulas are represented in a form of a finite sum over Bernoulli and Eulerian polynomials of higher order with periodic coefficients. A novel recursive relation for the Sylvester ...
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