Cote n° 152 · pages 2–9
· 7 displayed formulas · Catégorie des types de mots [dont arbres plans] : notes manuscrites (s.d.).
Inventory dating : [à partir de 1982]
Édition de démonstration
\[\text{nb.\ d'ordre réduit} \;=\; \sum_{\alpha \in \pi_0(\mathring{D} \smallsetminus K \cap \mathring{D})} \bigl(\operatorname{card}(\alpha \cap S) - 1\bigr)\]
LaTeX source
\[
\text{nb.\ d'ordre réduit} \;=\; \sum_{\alpha \in \pi_0(\mathring{D} \smallsetminus K \cap \mathring{D})} \bigl(\operatorname{card}(\alpha \cap S) - 1\bigr)
\]\[S \simeq \bar A / \rho_\Gamma\]
LaTeX source
\[ S \simeq \bar A / \rho_\Gamma \]
\[\bar A \ \xrightarrow{\ \mathrm{rd}\ }\ A(C) \qquad \text{ens.\ des arêtes de } C\]
LaTeX source
\[
\bar A \ \xrightarrow{\ \mathrm{rd}\ }\ A(C) \qquad \text{ens.\ des arêtes de } C
\]\[\bar A \times \{+1\} = \bar A(C)_+ \quad \bigl[\, = \mathrm{rd}(\bar A)\,\bigr]
\qquad
\bar A \times \{-1\} = \bar A(C)_- \quad \bigl[\, = \mathrm{rg}(\bar A)\,\bigr]\]
LaTeX source
\[
\bar A \times \{+1\} = \bar A(C)_+ \quad \bigl[\, = \mathrm{rd}(\bar A)\,\bigr]
\qquad
\bar A \times \{-1\} = \bar A(C)_- \quad \bigl[\, = \mathrm{rg}(\bar A)\,\bigr]
\]\[\Longrightarrow \quad
\rho_C(\mathrm{rd}\,\bar a) = \mathrm{rd}(\rho_\Gamma(\bar a)), \qquad
\rho_C(\mathrm{rg}\,\bar a) = \mathrm{rg}(\rho_\Gamma(\bar a))\]
LaTeX source
\[
\Longrightarrow \quad
\rho_C(\mathrm{rd}\,\bar a) = \mathrm{rd}(\rho_\Gamma(\bar a)), \qquad
\rho_C(\mathrm{rg}\,\bar a) = \mathrm{rg}(\rho_\Gamma(\bar a))
\]\[\sigma_\Gamma = \sigma_C, \qquad \rho_\Gamma = \rho_C\]
LaTeX source
\[ \sigma_\Gamma = \sigma_C, \qquad \rho_\Gamma = \rho_C \]
\[\begin{array}{rcl}
\bar A(\Gamma) & \longleftarrow & A(C)\\[2pt]
\sigma_\Gamma & \longleftrightarrow & \rho_C\\[2pt]
\rho_\Gamma \sigma_\Gamma & \longleftarrow & \rho_C\\[2pt]
\rho_\Gamma & \longleftarrow & \rho_C\,\sigma_C
\end{array}\]
LaTeX source
\[
\begin{array}{rcl}
\bar A(\Gamma) & \longleftarrow & A(C)\\[2pt]
\sigma_\Gamma & \longleftrightarrow & \rho_C\\[2pt]
\rho_\Gamma \sigma_\Gamma & \longleftarrow & \rho_C\\[2pt]
\rho_\Gamma & \longleftarrow & \rho_C\,\sigma_C
\end{array}
\]