I was looking for a standard name of the set $\{x \in A : x_1 \leq x_2 \leq \cdots \leq x_n\}$, where $A = [0,1]^n$ or $A = [0,\infty)^n$. I think I saw this recently, but now I cannot find it anywhere.
Thanks in advance.
I was looking for a standard name of the set $\{x \in A : x_1 \leq x_2 \leq \cdots \leq x_n\}$, where $A = [0,1]^n$ or $A = [0,\infty)^n$. I think I saw this recently, but now I cannot find it anywhere.
Thanks in advance.
The second one is a Weyl chamber, the first one a Weyl chamber (for the same root system) truncated at level 1.
In geometric terms this is an n-simplex called a Schläfli orthoscheme when $A = [0,1]^n$.
The case when $A = [0,\infty)^n$ is an unbounded convex region, but very similar to a simplex in that it is simply a limit of the simplex as coordinates of the first figure are scaled up. One may well refer to this figure as the non-negative cone of the respective $(n-1)$-simplex.
it is the weyl chamber for the symmetric group