Correction to: A Note on the Number of (Maximal) Antichains in the Lattice of Set Partitions

Set partitions and partition lattices are well-known objects in combinatorics and play an important role as a search space in many applied problems including ensemble clustering. Searching for antichains in such lattices is similar to that of in Boolean lattices. Counting the number of antichains in Boolean lattices is known as the Dedekind problem. In spite of the known asymptotic for the latter problem, the behaviour of the number of antichains in partition lattices has been paid less attention. In this short paper, we show how to obtain a few first numbers of antichains and maximal antichains in the partition lattices with the help of concept lattices and provide the reader with some related heuristic bounds. The results of our computational experiments confirm the known values and are also recorded in the Online Encyclopaedia of Integer Sequences (see https://oeis.org/A358041 ).