Affiliation: Universite Claude Bernard, Lyon
Email: jlnicola@in2p3.fr
Title Of Talk: Partitions without small parts
URLS:
igd.univ-lyon1.fr/~mosaki/
(see Mosaki Nicolas et Sarkozy partitions sans petites parts)
Abstract: Let r(n,m) (resp. q(n,m)) denote the number of partitions of n into parts (resp. into distinct parts) each of which is at least m. Improving on preceding results given by J. Dixmier, P. Erdos, M. Szalay, G. Freiman, J. Pitman and myself, E. Mosaki, A. Sarkozy and I have obtained an asymptotic estimate for log r(n,m) (and for log q(n,m)) according to the powers of n^(-1/2) if m << n^(1/2) and to the powers of m/n if m >> n^(1/2)) which is valid in the range 1 <= m <= n/(log n)^3. The main idea is to apply the saddle point method to the generating function, and then to use the Euler-MacLaurin sommation formula.
Last update made Thu Nov 11 15:06:23 EST 2004.
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