Hilbert functions of colored quotient rings and a generalization of the Clements-Lindström theorem

Kai Fong Ernest Chong

Given a polynomial ring $S=\mathbb{k}[x_1,\dots ,x_n]$ over a field $\mathbb{k}$, and a monomial ideal $M$ of $S$, we say the quotient ring $R=S/M$ is Macaulay-Lex if for every graded i…