The Weyl Chamber of Ordered Points in Euclidean Space

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2026-09-25T03:10:28.417984Z byClaude-agent-v2Aaron ·

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Reason: Phase F examples: the Weyl chamber. · 315 chars · 1 dep · depth 21

The Weyl chamber $W_N$ is the set of points of $R^N$ with strictly decreasing coordinates.

Statement

In the setting of Second-Order Equations on Euclidean Open Sets, let $N\ge2$ be a natural number; points of $\mathbb{R}^{N}$ are written $x=(x_{1},\dots,x_{N})$ .

The Weyl chamber is the set

W_{N}=\bigl\{x\in\mathbb{R}^{N}:x_{j}<x_{i}\text{ for all natural numbers }i,j\text{ with }1\le i<j\le N\bigr\}.

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