dimachine / KrewerasNonCrossPartAnti

Counting (maximal) antichains of non-crossing partitions

KrewerasNonCrossPartAnti

Counting (maximal) antichains in Kreweras lattice of non-crossing set partitions

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

OEIS sequences: https://oeis.org/A358390, https://oeis.org/A358391

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 Kreweras lattice

2. Counting of maximal antichains for n in {0, 1, 2, 3, 4, 5} (https://oeis.org/A358390)

3. Counting of antichains for n in {0, 1, 2, 3, 4, 5} (https://oeis.org/A358391)

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

• Germain Kreweras, "Sur les partitions non croisées d'un cycle", Discrete Mathematics, volume 1, number 4, pages 333–350, 1972.

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