Chain enumeration, partition lattices and polynomials with only real roots
Chain enumeration, partition lattices and polynomials with only real roots
The coefficients of the chain polynomial of a finite poset enumerate chains in the poset by their number of elements. The chain polynomials of the partition lattices and their standard type \(B\) analogues are shown to have only real roots. The real-rootedness of the chain polynomial is conjectured for all …