2014/09/04 by Vladimir Grujić, Grujić, Vladimir
Mathematics · #16T05 #52B20 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:16T05 #msc:52B20
paper · pdf · doi:10.48550/arxiv.1409.1420
new graphics, section 6 revised, the example 7.5 provided; final version
arxiv created 2017/05/16 · arxiv updated 2017/05/18
For a generalized permutohedron Q the enumerator F(Q) of positive lattice points in interiors of maximal cones of the normal fan ΣQ is a quasisymmetric function. We describe this function for the class of nestohedra as a Hopf algebra morphism from a combinatorial Hopf algebra of building sets. For the class of graph-associahedra the corresponding quasisymmetric function is a new isomorphism invariant of graphs. The obtained invariant is quite natural as it is the generating function of ordered colorings of graphs and satisfies the recurrence relation with respect to deletions of vertices.