Johann Selewa: Connections between algebra and combinatorics, using Stanley-Reisner rings

Abstract: We compute the multigraded Hilbert series, minimal free resolutions, Betti numbers, and the simplical homology, of the \SR rings of certain abstract simplicial complexes of graphs and their line graphs, and investigate possible connections between the graph and its line graph. We connect the algebra with the combinatorics, by defining a kind of symmetric polynomials in terms of orbits of the automorphism group of the graph, and see how these polynomials interplay with the Hilbert series and Betti numbers.