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References etc.

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Antti H S Laaksonen 2017-02-25 22:20:40 +02:00
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14
chapter22.tex
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@ -342,7 +342,8 @@ corresponds to the binomial coefficient formula.
\index{Catalan number} \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 number of valid
parenthesis expressions that consist of parenthesis expressions that consist of
$n$ left parentheses and $n$ right parentheses. $n$ left parentheses and $n$ right parentheses.
@ -678,7 +679,8 @@ elements should be changed.
\index{Burnside's lemma} \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 the number of combinations so that
only one representative is counted only one representative is counted
for each group of symmetric combinations. for each group of symmetric combinations.
@ -764,7 +766,10 @@ with 3 colors is
\index{Cayley's formula} \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 there are $n^{n-2}$ labeled trees
that contain $n$ nodes. that contain $n$ nodes.
The nodes are labeled $1,2,\ldots,n$, The nodes are labeled $1,2,\ldots,n$,
@ -827,7 +832,8 @@ be derived using Prüfer codes.
\index{Prüfer code} \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. $n-2$ numbers that describes a labeled tree.
The code is constructed by following a process The code is constructed by following a process
that removes $n-2$ leaves from the tree. that removes $n-2$ leaves from the tree.

10
list.tex
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@ -40,6 +40,11 @@
Nim, a game with a complete mathematical theory. Nim, a game with a complete mathematical theory.
\emph{Annals of Mathematics}, 3(1/4):35--39, 1901. \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} \bibitem{cod15}
Codeforces: On ''Mo's algorithm'', Codeforces: On ''Mo's algorithm'',
\url{http://codeforces.com/blog/entry/20032} \url{http://codeforces.com/blog/entry/20032}
@ -242,6 +247,11 @@
Shortest connection networks and some generalizations. Shortest connection networks and some generalizations.
\emph{Bell System Technical Journal}, 36(6):1389--1401, 1957. \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} \bibitem{q27}
27-Queens Puzzle: Massively Parallel Enumeration and Solution Counting. 27-Queens Puzzle: Massively Parallel Enumeration and Solution Counting.
\url{https://github.com/preusser/q27} \url{https://github.com/preusser/q27}