The Cohen-Macaulay Property of Affine Semigroup Rings in Dimension 2

Tony Se, Grant Serio

Let $k$ be a field and $x,y$ indeterminates over $k$. Let $R=k[x^a,x^{p_1}{y}^{s_1},\dots ,x^{p_t}{y}^{s_t},y^b]\subseteq k[x,y]$. We calculate the Hilbert polynomial of $(x^a,y^b)$.…