X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/rairo15.git/blobdiff_plain/006d3c5dcaf6d769591b2496d592e87066b0ec42..HEAD:/generating.tex

diff --git a/generating.tex b/generating.tex
index 7e41a7d..5b0d393 100644
--- 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.
 
-\begin{Theo}
+\begin{thrm}
 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:
-\begin{Theo}
+\begin{thrm}
 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.
@@ -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.
-\begin{Theo}
+\begin{thrm}
 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