Decompositions of the Boolean Lattice into Rank-symmetric Chains

[摘要] The Boolean lattice $2^{[n]}$ is the power set of $[n]$ ordered by inclusion. A chain $c_{0}\subset\cdots\subset c_{k}$ in $2^{[n]}$ is rank-symmetric, if $|c_{i}|+|c_{k-i}|=n$ for $i=0,\ldots,k$; and it is symmetric, if $|c_{i}|=(n-k)/2+i$. We show that

[学科分类] 离散数学和组合数学

[关键词] Chain decompositions;Boolean lattice