From 101a111e82a4b07c6c4ea3cb943b991c81a2a4ce Mon Sep 17 00:00:00 2001
From: Antti H S Laaksonen <ahslaaks@cs.helsinki.fi>
Date: Sat, 25 Feb 2017 22:20:40 +0200
Subject: [PATCH] References etc.

---
 chapter22.tex | 14 ++++++++++----
 list.tex      | 10 ++++++++++
 2 files changed, 20 insertions(+), 4 deletions(-)

diff --git a/chapter22.tex b/chapter22.tex
index e6fb642..bc9ba31 100644
--- a/chapter22.tex
+++ b/chapter22.tex
@@ -342,7 +342,8 @@ corresponds to the binomial coefficient formula.
 
 \index{Catalan number}
 
-The \key{Catalan number} $C_n$ 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.
@@ -678,7 +679,8 @@ elements should be changed.
 
 \index{Burnside's lemma}
 
-\key{Burnside's lemma} 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.
@@ -764,7 +766,10 @@ with 3 colors is
 
 \index{Cayley's formula}
 
-\key{Cayley's formula} 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 $1,2,\ldots,n$,
@@ -827,7 +832,8 @@ be derived using Prüfer codes.
 
 \index{Prüfer code}
 
-A \key{Prüfer code} 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.
diff --git a/list.tex b/list.tex
index 1131cfa..2a4082b 100644
--- a/list.tex
+++ b/list.tex
@@ -40,6 +40,11 @@
   Nim, a game with a complete mathematical theory.
   \emph{Annals of Mathematics}, 3(1/4):35--39, 1901.
 
+\bibitem{bur97}
+  W. Burnside.
+  \emph{Theory of Groups of Finite Order},
+  Cambridge University Press, 1897.
+
 \bibitem{cod15}
   Codeforces: On ''Mo's algorithm'',
   \url{http://codeforces.com/blog/entry/20032}
@@ -242,6 +247,11 @@
   Shortest connection networks and some generalizations.
   \emph{Bell System Technical Journal}, 36(6):1389--1401, 1957.
 
+\bibitem{pru18}
+  H. Prüfer.
+  Neuer Beweis eines Satzes über Permutationen.
+  \emph{Arch. Math. Phys}, 27:742--744, 1918.
+
 \bibitem{q27}
   27-Queens Puzzle: Massively Parallel Enumeration and Solution Counting.
   \url{https://github.com/preusser/q27}