The cd-index of the Boolean lattice

الأصل · EN

We study some properties of the cd-index of the Boolean lattice. They are extremely similar to the properties of the -index, or equivalently, the flag h-vector of the Boolean lattice and hence may be viewed as their cd-analogues. We define a different algebra structure on the polynomial algebra k <, > and give a derivation on this algebra. It is of significance for the Boolean lattice and forms our main tool. Using similar methods, we also prove some results for the cd-index of the cubical lattice. We show that the Dehn-Sommerville relations for the flag f-vector of an Eulerian poset are equivalent to certain simple identities that exist in our algebra.