Two classes of level Eulerian posets

TL;DR

This paper introduces two new classes of level Eulerian posets with specific cd-index properties and demonstrates that intervals in one class have order complexes homeomorphic to spheres.

Contribution

The paper defines two classes of level Eulerian posets with explicit cd-index formulas and topological properties for their intervals.

Findings

Intervals have cd-index as sum over monomials with coefficients r^{number of d's}

Order complexes of intervals in the first class are homeomorphic to spheres

Both classes contain intervals of rank k+1 with specified cd-index structure

Abstract

We present two classes of level Eulerian posets. Both classes contain intervals of rank k+1 whose cd-index is the sum over all cd-monomials w of degree k and the coefficient of the monomial w is r to the power of the number of d's in w. We also show that the order complexes of every interval in the first class are homeomorphic to spheres.