On Partition of a Boolean Lattice into Chains of Equal Sizes

Abstract

In this paper, we show that for every sufficiently large integer $n$ and every positive integer $c\le \lfloor \frac{1}{6}(\log \log n{)}^{\frac{1}{2}}\rfloor$, a Boolean lattice with $n$ atoms can be partitioned into chains of cardinality $c$, except for at most $c-1$ elements which also form a chain.