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Let $I$ be a graded ideal of $K[x_1,\ldots,x_n]$ generated by homogeneouspolynomials of a same degree $d$, and assume that $I$ has linear quotients. Inthis note, we use Horseshoe Lemma to give a relatively direct inductiveconstruction of a minimal free resolution of $I$, which is called a $d$-linearresolution.

Minimal free resolution of a graded ideal with linear quotients