diff --git a/fs-succinct/succinct.tex b/fs-succinct/succinct.tex index 406bcacd234ffbdbf5bd046e7950a7d4cd8eaf06..03c46d3145f5b47fa6657717e934f63a6955271d 100644 --- a/fs-succinct/succinct.tex +++ b/fs-succinct/succinct.tex @@ -202,7 +202,7 @@ for those too. For the second pass, this is trivial, as $(B+i)(B-i) = B^2 - i^2 \le B^2$. -\section{Succinct representation of arbitrary-alphabet strings} +\section{Mixers as a building block for succinct structures} \subsection{A reinterpretation of the SOLE encoding} @@ -334,7 +334,7 @@ as promised. Note that this holds for any value of $Y$. However, we cannot freely set $C$, as we have already decided that $C := \lfloor 2^M / Y \rfloor$. Instead, we need to set a value for $M$ that gives us the right $C$. -Now we are almost done. The whole mixer parameter selection process could be as follows +The whole mixer parameter selection process could be as follows (it may be useful to refer back to fig. \figref{mixer}): \tightlist{n.} \: We are given $X$, $Y$ as parameters. @@ -346,5 +346,6 @@ All the inequalities required for mixer existence are satisfied and based on the above the parameters satisfy what our lemma promised. \qed +\section{Succinct representation of arbitrary-alphabet strings} \endchapter