@inproceedings{DaeubelJaegerMuetzeScheucher2019,
Title = {On orthogonal symmetric chain decompositions},
Author = {D{\"a}ubel, Karl and J\"{a}ger, Sven and M{\"u}tze, Torsten and Scheucher, Manfred},
Booktitle = {Proceedings of the European Conference on Combinatorics, Graph Theory and Applications (EUROCOMB)},
Pages = {611--618},
Year = {2019},
Issn = {0862-9544},
Location = {Bratislava},
Journal = {Acta Mathematica Universitatis Comenianae},
Volume = {88},
Number = {3},
Month = {August},
Note = {extended abstract},
Editor = {Nešetřil, Jaroslav and Škoviera, Martin},
Abstract = {The n-cube is the poset obtained by ordering all subsets of {1,...,n} by inclusion, and it can be partitioned into n choose ⌊n/2⌋ chains, which is the minimum possible number. Two such decompositions of the n-cube are called orthogonal if any two chains of the decomposition share at most a single element. Shearer and Kleitman conjectured in 1979 that the n-cube has ⌊n/2⌋+1 pairwise orthogonal decompositions into the minimum possible number of chains, and they constructed two such decompositions. Spink recently improved this by showing that the n-cube has three pairwise orthogonal chain decompositions for n ≥ 24. In this paper, we construct four pairwise orthogonal chain decompositions of the n-cube for n ≥ 60. We also construct five pairwise edge-disjoint symmetric chain decompositions of the n-cube for n ≥ 90, where edge-disjointness is a slightly weaker notion than orthogonality, improving on a recent result by Gregor, Jäger, Mütze, Sawada, and Wille.},
Url2 = {http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1203}
}