The bounds for the number of linear extensions via chain and antichain coverings

I. A. Bochkov, F. V. Petrov

Let $(\mathcal{P},⩽)$ be a finite poset. Define the numbers $a_1,a_2,\dots$ (respectively, $c_1,c_2,\dots$) so that $a_1+\dots +a_k$ (respectively, $c_1+\dots +c_k$) is t…