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Given a polynomial ring $S = \Bbbk[x_1, \dots, x_n]$ over a field $\Bbbk$,and a monomial ideal $M$ of $S$, we say the quotient ring $R = S/M$ isMacaulay-Lex if for every graded ideal of $R$, there exists a lexicographicideal of $R$ with the same Hilbert function. In this paper, we introduce aclass of quotient rings with combinatorial significance, which we call coloredquotient rings. This class of rings include Clements-Lindstr\"om rings andcolored squarefree rings as special cases that are known to be Macaulay-Lex. Weconstruct two new classes of Macaulay-Lex rings, characterize all coloredquotient rings that are Macaulay-Lex, and give a simultaneous generalization ofboth the Clements-Lindstr\"om theorem and the Frankl-F\"uredi-Kalai theorem. Wealso show that the $f$-vectors of $(a_1, \dots, a_n)$-colored simplicialcomplexes or multicomplexes are never characterized by "reverse-lexicographic"complexes or multicomplexes when $n>1$ and $(a_1, \dots, a_n) \neq (1, \dots,1)$.

Hilbert functions of colored quotient rings and a generalization of the Clements-Lindstr\"om theorem