The Stacks project

  • are given by

    \[ \left( \begin{matrix} m_1 \\ m_2 \\ m_3 \\ m_4 \end{matrix} \right), \quad \left( \begin{matrix} -2w & w & 0 & 0 \\ w & -2w & 2w & 0 \\ 0 & 2w & -4w & 2w \\ 0 & 0 & 2w & -4w \end{matrix} \right), \quad \left( \begin{matrix} w \\ w \\ 2w \\ 2w \end{matrix} \right) \]

    with $2m_1 \geq m_2$, $2m_2 \geq m_1 + 2m_3$, $2m_3 \geq m_2 + m_4$, and $2m_4 \geq m_3$.

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