On some problems of J. Dénes and P. Turán

Abstract

In what follows we are dealing with some statistical properties of partitions resp. unequal partitions of positive integers. We introduce the notation

$$ \Pi = \left\{ {\begin{array}{*{20}{c}} {{\lambda _1} + {\lambda _2} + \ldots + {\lambda _m} = n} \\ {{\lambda _1} \geqq {\lambda _2} \geqq \ldots \geqq {\lambda _m} \geqq 1} \end{array}} \right\} $$

(1.1)

for a generic partition Π of n where

$$m = m(\Pi )\,and\,the\,\lambda _\mu 's\,are\operatorname{int} egers.$$

(1.2)