New Classes of Set-theoretic Complete Intersection Monomial Ideals

摘要

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