Sylvester Waves in the Coxeter Groups ∗

0 Sylvester Waves in the Coxeter Groups Leonid G . Fel

A new recursive procedure of the calculation of partition numbers function W (s,dm) is suggested. We find its zeroes and prove a lemma on the function parity properties. The explicit formulas of W (s,dm) and their periods τ(G) for the irreducible Coxeter groups and a list for the first ten symmetric group Sm are presented. A least common multiple L(m) of the series of the natural numbers 1,2,.....

Bases for modules of differential operators of order 2 on the classical Coxeter arrangements

It is well-known that the derivation modules of Coxeter arrangements are free. Holm began to study the freeness of modules of differential operators on hyperplane arrangements. In this paper, we study the cases of the Coxter arrangements of type A, B and D. In this case, we prove that the modules of differential operators of order 2 are free. We give examples of all the 3-dimensional classical ...

Complete Growth Series of Coxeter Groups with more than Three Generators

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 ...

Restricted Partition Functions as Bernoulli and Euler Polynomials of Higher Order

Explicit expressions for restricted partition function W (s,d) and its quasiperiodic components Wj(s,d ) (called Sylvester waves) for a set of positive integers d = {d1, d2, . . . , dm} are derived. The formulas are represented in a form of a finite sum over Bernoulli and Euler polynomials of higher order with periodic coefficients. A novel recursive relation for the Sylvester waves is establis...