THE cd-INDEX OF THE POSET OF INTERVALS AND Et-CONSTRUCTION

Given a graded poset P, let I(P) denote the associated poset of intervals and Et(P) the poset obtained from P by the Et-construction of Paffenholz and Ziegler [7]. We analyze how the ab-index behaves under those operations and prove that its change is expressed in terms of certain, quite explicit, recursively defined linear operators. If the poset P is Eulerian, the recursive relations for those linear operators are interpreted inside the coalgebra spanned by c and d. We use these relations to prove that the cd-index of the dual of the poset of intervals of the simplest Eulerian poset is the same as the cd-index of appropriate Tchebyshev poset defined by Hetyei in [5].