2009/11/11 by Hillary Einziger, Einziger, Hillary
Mathematics · #05E02 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.CO #msc:05E02
paper · pdf · doi:10.48550/arxiv.0911.2168
arxiv created 2010/04/27 · arxiv updated 2010/04/28
We present a new formula for the antipode of incidence Hopf algebras. This formula is expressed as an alternating sum over forests. First, we prove the formula for incidence Hopf algebras of families of lattices by exhibiting a map from chains of a lattice to forests. Then, we extend the definition and present an analogous formula for the antipode of incidence Hopf algebras of families of posets. We characterize those families for which our formula is cancellation-free.