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Let $Q$ be an affine monoid, $\Bbbk[Q]$ the associated monoid$\Bbbk$-algebra, and $\Bbbk[\overline{Q}]$ its normalization, where we let$\Bbbk$ be a field. In this paper, in the case where $\Bbbk[Q]$ is homogeneous(i.e., standard graded), a difference of the Hilbert series of $\Bbbk[Q]$ and$\Bbbk[\overline{Q}]$ is discussed. More precisely, we prove that if $\Bbbk[Q]$satisfies Serre's condition $(S_2)$, then the degree of the $h$-polynomial of$\Bbbk[Q]$ is always greater than or equal to that of $\Bbbk[\overline{Q}]$.Moreover, we also show counterexamples of this statement if we drop theassumption $(S_2)$.

Difference of Hilbert series of homogeneous monoid algebras and their normalizations