From recursions to asymptotics: on Szekeres' formula for the number of partitions
نویسنده
چکیده
We give a new proof of Szekeres’ formula for P (n, k), the number of partitions of the integer n having k or fewer positive parts. Our proof is based on the recursion satisfied by P (n, k) and Taylor’s formula. We make no use of the Cauchy integral formula or any complex variables. The derivation is presented as a step-by-step procedure, to facilitate its application in 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. AMS-MOS Subject Classification (1990). Primary: 05A17 Secondary: 05A20, 05A16, 11P81 the electronic journal of combinatorics 4 (no. 2) (1997), #R6 2
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ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 4 شماره
صفحات -
تاریخ انتشار 1997