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This paper concerns the study of a class of clutters called simplicialsubclutters. Given a clutter $\mathcal{C}$ and its simplicial subclutter$\mathcal{D}$, we compare some algebraic properties and invariants of theideals $I, J$ associated to these two clutters, respectively. We give a formulafor computing the (multi)graded Betti numbers of $J$ in terms of those of $I$and some combinatorial data about $\mathcal{D}$. As a result, we see that if$\mathcal{C}$ admits a simplicial subclutter, then there exists a monomial $u\notin I$ such that the (multi)graded Betti numbers of $I+(u)$ can be computedthrough those of $I$. It is proved that the Betti sequence of any graded idealwith linear resolution is the Betti sequence of an ideal associated to asimplicial subclutter of the complete clutter. These ideals turn out to havelinear quotients. However, they do not form all the equigenerated square-freemonomial ideals with linear quotients. If $\mathcal{C}$ admits $\varnothing$ asa simplicial subclutter, then $I$ has linear resolution over all fields.Examples show that the converse is not true.

Multigraded minimal free resolutions of simplicial subclutters