Partitions of \(n\) into \(t\sqrt n\) parts
\textit{G. Szekeres} [Q. J. Math., Oxf. II. Ser. 4, 96--111 (1953; Zbl 0050.04101)] used complex analysis to prove an asymptotic formula for \(P(n, k)\), the number of unordered partitions of \(n\) into at most \(k\) parts. \textit{E. R. Canfield} [Electron. J. Comb. 4, Research paper R6, 16p. (1997); printed version J. Comb. 4, 51--66 (1997; Zbl 0885.05015)] simplified the formula and avoided the use of complex analysis. Here the author proves this result again when \(k\) is at least a constant times \(\sqrt{n}\) using a central limit theorem of \textit{B. Fristedt} [Trans. Am. Math. Soc. 337, 703--735 (1993; Zbl 0795.05009)]. Using a probabilitistic approach he goes on to derive asympototics for the number of minimal difference \(d\) partitions with a given number of parts.
scientific article; zbMATH DE number 2126327