X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/16dcc.git/blobdiff_plain/e1fe6e435ee452003a7135763d26e2320756398c..6c611637ef05c993351fece7ff89ee10a2090031:/generating.tex?ds=sidebyside

diff --git a/generating.tex b/generating.tex
index ace2f7a..d512a98 100644
--- a/generating.tex
+++ b/generating.tex
@@ -45,10 +45,10 @@ cycle is removed, is doubly stochastic.
 Let us consider now a ${\mathsf{N}}$-cube where an Hamiltonian 
 cycle is removed.
 Let $f$ be the corresponding function.
-The question which remains to solve is
-can we always find $b$ such that $\Gamma_{\{b\}}(f)$ is strongly connected.
+The question which remains to solve is:
+\emph{can we always find $b$ such that $\Gamma_{\{b\}}(f)$ is strongly connected?}
 
-The answer is indeed positive. We furtheremore have the following strongest 
+The answer is indeed positive. We furthermore have the following strongest 
 result.
 \begin{thrm}
 There exist $b \in \Nats$ such that $\Gamma_{\{b\}}(f)$ is complete.
@@ -58,7 +58,7 @@ There is an arc $(x,y)$ in the
 graph $\Gamma_{\{b\}}(f)$ if and only if $M^b_{xy}$ is positive
 where $M$ is the Markov matrix of $\Gamma(f)$.
 It has been shown in~\cite[Lemma 3]{bcgr11:ip}  that $M$ is regular.
-There exists thus $b$ such there is an arc between any $x$ and $y$.
+Thus, there exists $b$ such that there is an arc between any $x$ and $y$.
 \end{proof}
 
 This section ends with the idea of removing a Hamiltonian cycle in the 
@@ -66,13 +66,20 @@ $\mathsf{N}$-cube.
 In such a context, the Hamiltonian cycle is equivalent to a Gray code.
 Many approaches have been proposed a way to build such codes, for instance 
 the Reflected Binary Code. In this one, one of the bits is switched 
-exactly $2^{\mathsf{N}-}$ for a $\mathsf{N}$-length cycle. 
+exactly $2^{\mathsf{N}-}$ \ANNOT{formule incomplète : $2^{\mathsf{N}-1}$ ??} for a $\mathsf{N}$-length cycle. 
 
 %%%%%%%%%%%%%%%%%%%%%
 
 The function that is built 
-from the 
+from the \ANNOT{Phrase non terminée}
 
 The next section presents how to build balanced Hamiltonian cycles in the 
 $\mathsf{N}$-cube with the objective to embed them into the 
 pseudorandom number generator.
+
+%%% Local Variables:
+%%% mode: latex
+%%% TeX-master: "main"
+%%% ispell-dictionary: "american"
+%%% mode: flyspell
+%%% End: