New inequalities for p ( n ) and log p ( n ) .

Let p ( n ) denote the number of partitions of n . A new infinite family of inequalities for p ( n ) is presented. This generalizes a result by William Chen et al. From this infinite family, another infinite family of inequalities for log p ( n ) is derived. As an application of the latter family one, for instance obtains that for n ≥ 120 , p ( n ) 2 > ( 1 + π 24 n 3 / 2 - 1 n 2 ) p ( n - 1 ) p ( n + 1 ) .