0 Sylvester Waves in the Coxeter Groups Leonid G . Fel
نویسندگان
چکیده
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,..,m plays a role of the period τ(Sm) of W (s,dm) in Sm. An asymptotic behaviour of L(m) with m → ∞ is found. Pacs: Number theory, Invariant theory
منابع مشابه
Sylvester Waves in the Coxeter Groups ∗
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 τ (G) for the irreducible Coxeter groups and a list for the first twelve symmetric group S m are presented. A least common multiple lcm(m) of the series of the natural num...
متن کاملRestricted 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 ...
متن کاملRestricted 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...
متن کاملCat(0) Groups and Coxeter Groups Whose Boundaries Are Scrambled Sets
In this paper, we study CAT(0) groups and Coxeter groups whose boundaries are scrambled sets. Suppose that a group G acts geometrically (i.e. properly and cocompactly by isometries) on a CAT(0) space X. (Such group G is called a CAT(0) group.) Then the group G acts by homeomorphisms on the boundary ∂X of X and we can define a metric d∂X on the boundary ∂X. The boundary ∂X is called a scrambled ...
متن کاملOn Summatory Totient Functions
The function F [kuφv, N ] has been the subject of intensive study for the last century and is classically known [2] for u ≤ 0, v = 1. The other results include u = 0, v = −1 [8], v = −u > 0 [4], [3] and references therein, v ≥ 0, u < −v − 1 [6], u = 1, v = −1 [10], [15], u = v = −1 [9], [17]. The leading and error terms for u = 0, v ∈ Z+, were calculated in [4] and [3], respectively. An extensi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008