Geodesic
From recursions to asymptotics: On Szekeres' formula for the number of partitions
The electronic journal of combinatorics, The Wilf Festschrift volume, Tome 4 (1997) no. 2
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

We give a new proof of Szekeres' formula for $P(n,k)$, the number of partitions of the integer $n$ having $k$ or fewer parts. Our proof is based on the recursion formula satisfied by $P(n,k)$ and Taylor's formula. We make no use of the Cauchy integral formula or complex variables. The derivation is presented as a step-by-step procedure, to facilitate its applicationin other situations. As corollaries we obtain the main term of the Hardy-Ramanujan formulas for $p(n)=$ the number of unrestricted partitions of $n$ and for $q(n)=$ the number of partitions of $n$ into distinct parts.
DOI : 10.37236/1321
Classification : 05A17, 05A20, 05A16, 11P81
Mots-clés : partitions, Hardy-Ramanujan formulas 
@article{10_37236_1321,
     author = {E. Rodney Canfield},
     title = {From recursions to asymptotics: {On} {Szekeres'} formula for the number of partitions},
     journal = {The electronic journal of combinatorics},
     year = {1997},
     volume = {4},
     number = {2},
     doi = {10.37236/1321},
     zbl = {0885.05015},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1321/}
}
TY  - JOUR
AU  - E. Rodney Canfield
TI  - From recursions to asymptotics: On Szekeres' formula for the number of partitions
JO  - The electronic journal of combinatorics
PY  - 1997
VL  - 4
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.37236/1321/
DO  - 10.37236/1321
ID  - 10_37236_1321
ER  - 
%0 Journal Article
%A E. Rodney Canfield
%T From recursions to asymptotics: On Szekeres' formula for the number of partitions
%J The electronic journal of combinatorics
%D 1997
%V 4
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/1321/
%R 10.37236/1321
%F 10_37236_1321
E. Rodney Canfield. From recursions to asymptotics: On Szekeres' formula for the number of partitions. The electronic journal of combinatorics, The Wilf Festschrift volume, Tome 4 (1997) no. 2. doi: 10.37236/1321

Cité par Sources :