Definition:Product of Differences

Definition

Let $n \in \Z, n > 0$ be an integer.

Then $\Delta_n \left({x_1, x_2, \ldots, x_n}\right)$ is defined as:

$\displaystyle \Delta_n = \prod_{1 \le i < j \le n} \left({x_i - x_j}\right)$

Thus $\Delta_n$ is the product of the difference of all pairs of $\left\{{x_1, x_2, \ldots, x_n}\right\}$ where the index of the first is less than the index of the second.

Sources

• J.A. Green: Sets and Groups (1965)... (previous)... (next): $\S 7.4$: Example $142$
• John F. Humphreys: A Course in Group Theory (1996): $\S 9$: Definition $9.14$