The cone of Hilbert functions in the non-standard graded case

Abstract

We describe the cone of Hilbert functions of artinian graded modules finitely generated in degree 0 over the polynomial ring R = k[x, y] with the non-standard grading deg(x) = 1 and deg(y) = n, where n is any natural number.

Keywords

• Artinian modules
• Cone of hilbert functions
• Graded rings and modules
• Lex-segment ideals