Mediant hull: Difference between revisions
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<math>T_1 \mid\mid T_2 \mid\mid \cdots \mid\mid T_n = \operatorname{cl}\bigg\{\dfrac{a_1 m_1 + \cdots + a_r m_r}{a_1 n_1 + \cdots + a_r n_r} : (a_1, ..., a_r) \in \mathbb{Z}^r_{\geq 0} \setminus (0, 0, ..., 0) \bigg\}</math> | <math>T_1 \mid\mid T_2 \mid\mid \cdots \mid\mid T_n = \operatorname{cl}\bigg\{\dfrac{a_1 m_1 + \cdots + a_r m_r}{a_1 n_1 + \cdots + a_r n_r} : (a_1, ..., a_r) \in \mathbb{Z}^r_{\geq 0} \setminus (0, 0, ..., 0) \bigg\}</math> | ||
where <math>\operatorname{cl}</math> denotes the topological closure (specifying the generator is enough, given the period). The generalization to higher-rank scale structures is obvious. | where <math>\operatorname{cl}</math> denotes the topological closure (specifying the generator is enough, given the period, since the period doesn't change upon taking the mediant). The generalization to higher-rank scale structures is obvious. | ||
== Notation == | == Notation == | ||