Partitioning Boolean lattices into antichains

Authors:
Muktar Elzobi;Zbigniew Lonc
Affiliations:
Department of Mathematics and Information Sciences, Warsaw University of Technology, 00-661 Warsaw, Poland;Department of Mathematics and Information Sciences, Warsaw University of Technology, 00-661 Warsaw, Poland
Venue:
Discrete Mathematics
Year:
2003

Citing 3
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Abstract

Let f(n) be the smallest integer t such that a poset obtained from a Boolean lattice with n atoms by deleting both the largest and the smallest elements can be partitioned into t antichains of the same size except for possibly one antichain of a smaller size. In this paper, it is shown that f(n) ≤ bn2/log n. This is an improvement of the best previously known upper bound for f(n).