Four-element generating sets of partition lattices and their direct products

Limit laws of weighted power sums of extreme values and Statistical analysis of partition lattices

“…This chapter entails investigating four-element generating sets of a partition lattice and establishing a lower bound for the number of four-element generating sets of direct products of two neighbouring partition lattices. The chapter is divided into four sections, which are taken from [26] and [63]. Section 1 is introductory and combines the corresponding parts of [26] and [63].…”

“…The chapter is divided into four sections, which are taken from [26] and [63]. Section 1 is introductory and combines the corresponding parts of [26] and [63]. Sections 2 and 3 are reprints from [26].…”

“…Section 1 is introductory and combines the corresponding parts of [26] and [63]. Sections 2 and 3 are reprints from [26]. Section 4 is taken from [63] but more details are given here.…”

“…Also, there is a notational change in Section 4: ν(n) from [63] has been changed to ν 2 (n) in order to avoid confusion with Sections 2 and 3, which inherit the meaning of ν(n) from [26]. The papers and results mentioned above were devoted to the existence of fourelement generating sets.…”

“…The study of the number of small generating sets of partition lattices have started recently with Czédli [25] and Czédli and Oluoch [26].…”