Martin–Reiner: cyclotomic and simplicial matroids

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Library card, especially Theorem 1 and Corollary 2.

Jeremy Martin and Victor Reiner, "Cyclotomic and simplicial matroids," Israel Journal of Mathematics 150 (2005), 229--240.

The paper identifies the rational linear-dependence matroid of the $n$-th roots of unity with the dual of a direct sum of $n/(p_1\cdots p_r)$ copies of a natural simplicial matroid determined by the distinct primes $p_1,\ldots,p_r$ dividing $n$ (Theorem 1, p. 2). When $n$ has two distinct prime factors $p_1,p_2$ that simplicial matroid is the graphic matroid of $K_{p_1,p_2}$, so the roots-of-unity matroid is cographic; in that case the paper also derives a generating function for the independent root subsets (Corollary 9, p. 7).