Global Constraint Catalog

$𝐌𝐀𝐗_𝐍𝐂𝐂$ , $𝐌𝐈𝐍_𝐍𝐂𝐂$ , $𝐍𝐀𝐑𝐂$ , $𝐍𝐂𝐂$ , $𝐍𝐕𝐄𝐑𝐓𝐄𝐗$

Proposition 123

Let:

\begin{matrix} Δ = 0 \lor (𝐌𝐀𝐗_𝐍𝐂𝐂 \neq 𝐌𝐈𝐍_𝐍𝐂𝐂 \land δ + ϵ \leq 𝐍𝐂𝐂) \end{matrix}

\begin{matrix} 𝐍𝐀𝐑𝐂 \leq (𝐍𝐂𝐂 - δ - ϵ) \cdot 𝐌𝐈𝐍_{𝐍𝐂𝐂}^{2} + ϵ \cdot {(𝐌𝐈𝐍_𝐍𝐂𝐂 + r)}^{2} + δ \cdot 𝐌𝐀𝐗_{𝐍𝐂𝐂}^{2} \end{matrix}

Proposition 123 is currently a conjecture.

$𝐌𝐈𝐍_𝐍𝐂𝐂$ , $𝐍𝐀𝐑𝐂$ , $𝐍𝐂𝐂$ , $𝐍𝐒𝐂𝐂$ , $𝐍𝐕𝐄𝐑𝐓𝐄𝐗$

Proposition 124

\begin{matrix} 𝐍𝐀𝐑𝐂 \leq & (𝐍𝐂𝐂 - 1) \cdot max (1, (𝐌𝐈𝐍_𝐍𝐂𝐂 - 1)) + \\ (𝐍𝐕𝐄𝐑𝐓𝐄𝐗 - 𝐍𝐒𝐂𝐂 + 1) \cdot (𝐍𝐕𝐄𝐑𝐓𝐄𝐗 - 𝐍𝐂𝐂 + 1) + \\ \frac{(𝐍𝐒𝐂𝐂 - 𝐍𝐂𝐂 + 1) \cdot (𝐍𝐒𝐂𝐂 - 𝐍𝐂𝐂)}{2} \end{matrix}

Proposition 124 is currently a conjecture.

4. Further Topics