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Omni-MATH / The set of points (x₁,x₂,x₃,x₄) in R⁴ such that x₁≥x₂≥x₃≥x₄ is a cone (or hypercone, if you insist). Into how many regions is this cone sliced by the hyperplanes x_(i)−x_(j)=1 for …

Problem

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problem

The set of points (x1,x2,x3,x4)\left(x_{1}, x_{2}, x_{3}, x_{4}\right) in R4\mathbf{R}^{4} such that x1≥x2≥x3≥x4x_{1} \geq x_{2} \geq x_{3} \geq x_{4} is a cone (or hypercone, if you insist). Into how many regions is this cone sliced by the hyperplanes xi−xj=1x_{i}-x_{j}=1 for 1≤i<j≤n1 \leq i<j \leq n ?
Plain-text mathematical notation (without MathML)
The set of points (x₁,x₂,x₃,x₄) in R⁴ such that x₁≥x₂≥x₃≥x₄ is a cone (or hypercone, if you insist). Into how many regions is this cone sliced by the hyperplanes x_(i)−x_(j)=1 for 1≤i<j≤n ?
Original LaTeX notation
The set of points $\left(x_{1}, x_{2}, x_{3}, x_{4}\right)$ in $\mathbf{R}^{4}$ such that $x_{1} \geq x_{2} \geq x_{3} \geq x_{4}$ is a cone (or hypercone, if you insist). Into how many regions is this cone sliced by the hyperplanes $x_{i}-x_{j}=1$ for $1 \leq i<j \leq n$ ?

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Source and history

task_id
31c56bc0-3dcd-52da-99ad-c4ba6814c8fd
task_key
test--31c56bc0-3dcd-52da-99ad-c4ba6814c8fd
task_revision_id
1
config / split
/ test

Official source

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