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Restricted partition as Bernoulli polynomials of higher orderAlgebra & Discrete Mathematics
|Speaker: ||Boris Rubinstein, UC Davis|
|Location: ||693 Kerr|
|Start time: |
Explicit expressions for restricted partition
function (Sylvester's denumerant) and its quasiperiodic components
(called Sylvester waves) for a set of positive
integers are derived.
I show an explicit formula for the
Sylvester wave in a form of finite sum of the Bernoulli
polynomials of higher
order multiplied by a periodic function of integer period. The periodic factor
is expressed through the
Eulerian polynomials of higher order (introduced by L.Carlitz).
I show that it is possible to represent this result also
in a form of a finite sum over
Bernoulli polynomials of higher order with periodic coefficients.