Algebras arising from bipartite planar graphs

Abstract

Let G be a bipartite planar graph and k[G] its associated monomial algebra. We find a linear system of parameters for k[G] and a maximal regular sequence in P(G), the presentation ideal of k[G]. This allows us to bound the coefficients of the Hubert series, and in some cases to compute it exactly. The techniques of the theory of Gröbner bases are used throughout.

^*Supported by UFRGS and CAPES (Proc. 2595/92-2).

^†Supported by DIMACS.

^*Supported by UFRGS and CAPES (Proc. 2595/92-2).

^†Supported by DIMACS.

Notes

^*Supported by UFRGS and CAPES (Proc. 2595/92-2).

^†Supported by DIMACS.