572 research outputs found
An Explicit Formula for Restricted Partition Function through Bernoulli Polynomials
Explicit expressions for restricted partition function and
its quasiperiodic components (called Sylvester waves) for a
set of positive integers are derived. The
formulas are represented in a form of a finite sum over Bernoulli polynomials
of higher order with periodic coefficients.Comment: 8 pages, submitted to The Ramanujan Journa
Elimination Theory in Codimension Two
New formulas are given for Chow forms, discriminants and resultants arising
from (not necessarily normal) toric varieties of codimension 2. Exact
descriptions are also given for the secondary polygon and for the Newton
polygon of the discriminant.Comment: 20 pages, Late
Extension of the Bernoulli and Eulerian Polynomials of Higher Order and Vector Partition Function
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 , i.e., a number of integer solutions to a linear
system . It is shown that can be expressed through the vector Bernoulli polynomials of higher order.Comment: 18 page
- …