SetPartAnti

Counting (maximal) antichains in the lattice of set partitions

This is a supporing file for OEIS on computation of (maximal) antichains in the lattice of set partitions.

Outline

0. The basic code with the class for managing generation of formal concepts via NextClosure algorithm

1. Loading formal contexts for antichains and maximal antichains of a partition lattice

2. Counting of maximal antichains for n in {0, 1, 2, 3, 4, 5}

3. Counting of antichains for n in {0, 1, 2, 3, 4, 5} (https://oeis.org/A302250)

Comment to Sections 2 and 3.

We start with n=0 (i.e., with the set partition of zero elements), but in OEIS the respective offset is 1, i.e. there the sequences start with n=1.

References

• Bernhard Ganter, Rudolf Wille: Formal Concept Analysis - Mathematical Foundations. Springer 1999, ISBN 978-3-540-62771-5, pp. I-X, 1-284

• Graham, R.L. Maximum antichains in the partition lattice. The Mathematical Intelligencer 1, 84–86 (1978). https://doi.org/10.1007/BF03023067

NB. Any usage of the codes requires the acknowledgment of this repository.