Some fixes

chapter22.tex

@@ -342,8 +342,9 @@ corresponds to the binomial coefficient formula.
 
 \index{Catalan number}
 
-The \key{Catalan number}\footnote{E. C. Catalan (1814--1894)
-was a Belgian mathematician.} $C_n$ equals the
+The \key{Catalan number}
+%\footnote{E. C. Catalan (1814--1894) was a Belgian mathematician.}
+$C_n$ equals the
 number of valid
 parenthesis expressions that consist of
 $n$ left parentheses and $n$ right parentheses.
@@ -679,8 +680,9 @@ elements should be changed.
 
 \index{Burnside's lemma}
 
-\key{Burnside's lemma}\footnote{Actually, Burnside did not discover this lemma;
-he only mentioned it in his book \cite{bur97}.} can be used to count
+\key{Burnside's lemma}
+%\footnote{Actually, Burnside did not discover this lemma; he only mentioned it in his book \cite{bur97}.}
+can be used to count
 the number of combinations so that
 only one representative is counted
 for each group of symmetric combinations.
@@ -766,10 +768,10 @@ with 3 colors is
 
 \index{Cayley's formula}
 
-\key{Cayley's formula}\footnote{While the formula
-is named after A. Cayley,
-who studied it in 1889,
-it was discovered earlier by C. W. Borchardt in 1860.} states that
+\key{Cayley's formula}
+% \footnote{While the formula is named after A. Cayley,
+% who studied it in 1889, it was discovered earlier by C. W. Borchardt in 1860.}
+states that
 there are $n^{n-2}$ labeled trees
 that contain $n$ nodes.
 The nodes are labeled $1,2,\ldots,n$,
@@ -832,8 +834,9 @@ be derived using Prüfer codes.
 
 \index{Prüfer code}
 
-A \key{Prüfer code}\footnote{In 1918, H. Prüfer proved
-Cayley's theorem using Prüfer codes \cite{pru18}.} is a sequence of
+A \key{Prüfer code}
+%\footnote{In 1918, H. Prüfer proved Cayley's theorem using Prüfer codes \cite{pru18}.}
+is a sequence of
 $n-2$ numbers that describes a labeled tree.
 The code is constructed by following a process
 that removes $n-2$ leaves from the tree.