Sylvester Waves in the Coxeter Groups |
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| Authors: | Fel Leonid G Rubinstein Boris Y |
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| Institution: | (1) School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, 69978, Israel;(2) Department of Engineering Sciences and Applied Mathematics, Northwestern University, 2145 Sheridan Road, Evanston, Illinois, 60208-3125 |
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| Abstract: | A new recursive procedure of the calculation of partition numbers function W(s, d
m
) is suggested. We find its zeroes and prove a lemma on the function parity properties. The explicit formulas of W(s, d
m
) and their periods  (G) for the irreducible Coxeter groups and a list for the first twelve symmetric group
m
are presented. A least common multiple
(m) of the series of the natural numbers 1,2,...,m plays a role in the period (
m
) of W(s, d
m) in
m
. |
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| Keywords: | partitions asymptotic of arithmetic functions Coxeter groups |
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