2002/11/25 by Swapneel Mahajan, Mahajan, Swapneel
Mathematics · #05A20 (Primary) 06A11 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A20 #msc:06A11
paper · pdf · doi:10.48550/arxiv.math/0211390
arxiv created 2002/11/25 · arxiv updated 2009/11/30
We study some properties of the \bf cd-index of the Boolean lattice. They are extremely similar to the properties of the \ab-index, or equivalently, the flag h-vector of the Boolean lattice and hence may be viewed as their \bf cd-analogues. We define a different algebra structure on the polynomial algebra k < \cv, \dv> 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 \bf 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.