Gotzmann Edge Ideals
Let P = k[x_1, ..., x_n] be the polynomial ring in n variables. A homogeneous ideal I of P generated in degree d is called Gotzmann if it has the smallest possible Hilbert function out of all homogeneous ideals with the same dimension in degree d. The edge ideal of a simple graph G on vertices x_1,...
Saved in:
Main Author | |
---|---|
Format | Journal Article |
Language | English |
Published |
13.08.2009
|
Subjects | |
Online Access | Get full text |
Cover
Loading…
Summary: | Let P = k[x_1, ..., x_n] be the polynomial ring in n variables. A homogeneous
ideal I of P generated in degree d is called Gotzmann if it has the smallest
possible Hilbert function out of all homogeneous ideals with the same dimension
in degree d. The edge ideal of a simple graph G on vertices x_1, ..., x_n is
the quadratic square-free monomial ideal generated by all x_i x_j where
{x_i,x_j} is an edge of G. The only edge ideals that are Gotzmann are those
edge ideals corresponding to star graphs. |
---|---|
DOI: | 10.48550/arxiv.0908.1946 |