ajout espace bib

[rairo15.git] / generating.tex

diff --git a/generating.tex b/generating.tex
index 7e41a7dcb68fb5c2f2084c86d29a01f9c7e003ae..5b0d3931f3e51269806ef6df83a11a0731408304 100644 (file)
--- a/generating.tex
+++ b/generating.tex
@@ -29,19 +29,19 @@ states that the ${\mathsf{N}}$-cube without one
 Hamiltonian cycle 
 has the awaited property with regard to the connectivity.
 
 Hamiltonian cycle 
 has the awaited property with regard to the connectivity.
 

-\begin{Theo}
+\begin{thrm}

 The iteration graph $\Gamma(f)$ issued from
 the ${\mathsf{N}}$-cube where an Hamiltonian 
 cycle is removed is strongly connected.
 The iteration graph $\Gamma(f)$ issued from
 the ${\mathsf{N}}$-cube where an Hamiltonian 
 cycle is removed is strongly connected.

-\end{Theo}
+\end{thrm}

 
 Moreover, if all the transitions have the same probability ($\frac{1}{n}$),
 we have proven the following results:
 
 Moreover, if all the transitions have the same probability ($\frac{1}{n}$),
 we have proven the following results:

-\begin{Theo}
+\begin{thrm}

 The Markov Matrix $M$ resulting from the ${\mathsf{N}}$-cube in
 which an Hamiltonian 
 cycle is removed, is doubly stochastic.
 The Markov Matrix $M$ resulting from the ${\mathsf{N}}$-cube in
 which an Hamiltonian 
 cycle is removed, is doubly stochastic.

-\end{Theo}
+\end{thrm}

 
 Let us consider now a ${\mathsf{N}}$-cube where an Hamiltonian 
 cycle is removed.
 
 Let us consider now a ${\mathsf{N}}$-cube where an Hamiltonian 
 cycle is removed.


@@ -51,9 +51,9 @@ can we always find $b$ such that $\Gamma_{\{b\}}(f)$ is strongly connected.
 
 The answer is indeed positive. We furtheremore have the following strongest 
 result.
 
 The answer is indeed positive. We furtheremore have the following strongest 
 result.

-\begin{Theo}
+\begin{thrm}

 There exist $b \in \Nats$ such that $\Gamma_{\{b\}}(f)$ is complete.
 There exist $b \in \Nats$ such that $\Gamma_{\{b\}}(f)$ is complete.

-\end{Theo}
+\end{thrm}

 \begin{proof}
 There is an arc $(x,y)$ in the 
 graph $\Gamma_{\{b\}}(f)$ if and only if $M^b_{xy}$ is positive
 \begin{proof}
 There is an arc $(x,y)$ in the 
 graph $\Gamma_{\{b\}}(f)$ if and only if $M^b_{xy}$ is positive