A forest formula for the antipode in incidence Hopf algebras

Details A forest formula for the antipode in incidence Hopf algebras A forest formula for the antipode in incidence Hopf algebras

2009-11-11

arxiv.org/abs/0911.2168v2

Mathematics

Combinatorics

Scientific paper

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.

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