Sylvester Waves in the Coxeter Groups

2000/05/17 by Leonid G. Fel, Fel, Leonid G., Boris Rubinstein +2
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.math/0005174

One figure, 21 pages, submitted to Quart. J. Math

arxiv created 2000/05/17 · openalex publication_date 2000/05/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A new recursive procedure of the calculation of partition numbers function W(s,\bf d^m) is suggested. We find its zeroes and prove a lemma on the function parity properties. The explicit formulas of W(s,\bf d^m) and their periods τ(G) for the irreducible Coxeter groups and a list for the first ten symmetric group \cal S_m are presented. A \it least common multiple \cal L(m) of the series of the natural numbers 1,2,..,m plays a role of the period τ(\cal S_m) of W(s,\bf d^m) in \cal S_m. An asymptotic behaviour of \cal L(m) with m → ∞ is found.

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