Cross-set scale: Difference between revisions
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A '''cross-set scale''' is a [[scale]] generated by taking every ordered pair in the [[Wikipedia:Cartesian product|Cartesian product]] of two or more scales, or of a scale with itself, and stacking all elements in each ordered pair: | A '''cross-set scale''' is a [[scale]] generated by taking every ordered pair in the [[Wikipedia:Cartesian product|Cartesian product]] of two or more scales, or of a scale with itself, and stacking all elements in each ordered pair: | ||
<math>\text{Cross-set}(A, B, ..., Z) = \{ a + b + \cdots + z : (a, b, ..., z) \in A \times B \times \cdots \times Z\}</math> | <math>\text{Cross-set}(A, B, ..., Z) = \{ a + b + \cdots + z : (a, b, ..., z) \in A \times B \times \cdots \times Z\}.</math> | ||
In combinatorics, this operation is called a [[wikipedia:Sumset|sumset]]. | In combinatorics, this operation is called a [[wikipedia:Sumset|sumset]]. | ||