Estimates on binomial sums of partition functions

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Let p(n) denote the partition function and define p(n, k) = (Formula presenting) p(j) where p(0) = 1. We prove that p(n, k) is unimodal and satisfies p(n, k) <2.825/vn 2n for fixed n = 1 and all 1 = k = n. This result has an interesting application: the minimal dimension of a faithful module for a k-step nilpotent Lie algebra of dimension n is bounded by p(n, k) and hence by 3/vn 2n, independently of k. So far only the bound nn-1 as known. We will also prove that p (n, n-1) <vn exp(p v2n/3) for n = 1 and p(n - 1, n - 1) <exp(p v2n/3).
Seiten (von - bis)435-446
FachzeitschriftManuscripta Mathematica
PublikationsstatusVeröffentlicht - 2000

ÖFOS 2012

  • 1010 Mathematik