The number of symmetric chain decompositions

Abstract

We prove that the number of symmetric chain decompositions of the Boolean lattice $2^{[n]}$ is $${\left(\frac{n}{2e}+o(n)\right)}^{2^n}.$$ Furthermore, the number of symmetric chain decompositions of the hypergrid $[t{]}^n$ is $$n^{(1-o_n(1))\cdot t^n}.$$

arXiv comment7 pages