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arXiv · 0908.1946

Gotzmann Edge Ideals

Andrew H. Hoefel
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Abstract

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.

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Andrew H. Hoefel. 2009-08-13. Gotzmann Edge Ideals. https://arxiv.org/abs/0908.1946

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