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| Paper IPM / M / 13515 |
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Let ∆ be a simplicial complex and χ be an s-coloring of
∆. Biermann and Van Tuyl have introduced the simplicial complex
∆χ. As a corollary of Theorems 5 and 7 in their 2013 article,
we obtain that the Stanley-Reisner ring of ∆χ over a field
is Cohen-Macaulay. In this note, we generalize this corollary by proving
that the Stanley-Reisner ideal of ∆χ over a field is
set-theoretic complete intersection. This also generalizes a result of
Macchia.
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