\begin{thebibliography}{35}
\expandafter\ifx\csname natexlab\endcsname\relax\def\natexlab#1{#1}\fi
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  \def\bibnamefont#1{#1}\fi
\expandafter\ifx\csname bibfnamefont\endcsname\relax
  \def\bibfnamefont#1{#1}\fi
\expandafter\ifx\csname citenamefont\endcsname\relax
  \def\citenamefont#1{#1}\fi
\expandafter\ifx\csname url\endcsname\relax
  \def\url#1{\texttt{#1}}\fi
\expandafter\ifx\csname urlprefix\endcsname\relax\def\urlprefix{URL }\fi
\providecommand{\bibinfo}[2]{#2}
\providecommand{\eprint}[2][]{\url{#2}}

\bibitem[{\citenamefont{Abe}(2004)}]{AbeBook}
\bibinfo{author}{\bibnamefont{Abe}, \bibfnamefont{E.}}, \bibinfo{year}{2004},
  \emph{\bibinfo{title}{Hopf Algebras}} (\bibinfo{publisher}{Cambridge
  University Press}).

\bibitem[{\citenamefont{Aigner}(2007)}]{AignerBook}
\bibinfo{author}{\bibnamefont{Aigner}, \bibfnamefont{M.}},
  \bibinfo{year}{2007}, \emph{\bibinfo{title}{A Course in Enumeration}},
  Graduate Texts in Mathematics (\bibinfo{publisher}{Springer-Verlag},
  \bibinfo{address}{Berlin}).

\bibitem[{\citenamefont{Artin}(1991)}]{ArtinBook}
\bibinfo{author}{\bibnamefont{Artin}, \bibfnamefont{M.}}, \bibinfo{year}{1991},
  \emph{\bibinfo{title}{Algebra}} (\bibinfo{publisher}{Prentica Hall}).

\bibitem[{\citenamefont{Baez and Dolan}(2001)}]{Baez}
\bibinfo{author}{\bibnamefont{Baez}, \bibfnamefont{J.}}, and
  \bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Dolan}},
  \bibinfo{year}{2001}, in \emph{\bibinfo{booktitle}{Mathematics {U}nlimited -
  2001 and {B}eyond}} (\bibinfo{publisher}{Springer Verlag},
  \bibinfo{address}{Berlin}), pp. \bibinfo{pages}{29--50},
  \bibinfo{note}{ar{X}iv:math.QA/0004133 [math.QA]}.

\bibitem[{\citenamefont{Ballestoros}
  \emph{et~al.}(1997)\citenamefont{Ballestoros, Herranz, and
  Parashar}}]{Ballestoros}
\bibinfo{author}{\bibnamefont{Ballestoros}, \bibfnamefont{A.}},
  \bibinfo{author}{\bibfnamefont{F.~J.} \bibnamefont{Herranz}}, and
  \bibinfo{author}{\bibfnamefont{P.}~\bibnamefont{Parashar}},
  \bibinfo{year}{1997}, \bibinfo{journal}{J. Phys. A: Math. Gen.}
  \textbf{\bibinfo{volume}{30}}, \bibinfo{pages}{L149}.

\bibitem[{\citenamefont{Bergeron} \emph{et~al.}(1998)\citenamefont{Bergeron,
  Labelle, and Leroux}}]{BergeronBook}
\bibinfo{author}{\bibnamefont{Bergeron}, \bibfnamefont{F.}},
  \bibinfo{author}{\bibfnamefont{G.}~\bibnamefont{Labelle}}, and
  \bibinfo{author}{\bibfnamefont{P.}~\bibnamefont{Leroux}},
  \bibinfo{year}{1998}, \emph{\bibinfo{title}{Combinatorial Species and
  Tree-like Structures}} (\bibinfo{publisher}{Cambridge University Press},
  \bibinfo{address}{Cambridge}).

\bibitem[{\citenamefont{Bjorken and Drell}(1993)}]{BjorkenDrell}
\bibinfo{author}{\bibnamefont{Bjorken}, \bibfnamefont{J.~D.}}, and
  \bibinfo{author}{\bibfnamefont{S.~D.} \bibnamefont{Drell}},
  \bibinfo{year}{1993}, \emph{\bibinfo{title}{Relativistic Quantum Fields}}
  (\bibinfo{publisher}{McGraw-Hill}, \bibinfo{address}{New York}).

\bibitem[{\citenamefont{Blasiak} \emph{et~al.}(2007)\citenamefont{Blasiak,
  Horzela, Penson, Solomon, and Duchamp}}]{AmJPhys}
\bibinfo{author}{\bibnamefont{Blasiak}, \bibfnamefont{P.}},
  \bibinfo{author}{\bibfnamefont{A.}~\bibnamefont{Horzela}},
  \bibinfo{author}{\bibfnamefont{K.~A.} \bibnamefont{Penson}},
  \bibinfo{author}{\bibfnamefont{A.~I.} \bibnamefont{Solomon}}, and
  \bibinfo{author}{\bibfnamefont{G.~H.~E.} \bibnamefont{Duchamp}},
  \bibinfo{year}{2007}, \bibinfo{journal}{Am. J. Phys.}
  \textbf{\bibinfo{volume}{75}}, \bibinfo{pages}{639},
  \bibinfo{note}{ar{X}iv:0704.3116 [quant-ph]}.

\bibitem[{\citenamefont{Bourbaki}(1998)}]{BourbakiAlgebraI}
\bibinfo{author}{\bibnamefont{Bourbaki}, \bibfnamefont{N.}},
  \bibinfo{year}{1998}, \emph{\bibinfo{title}{Algebra}},
  volume~\bibinfo{volume}{I} (\bibinfo{publisher}{Springer}).

\bibitem[{\citenamefont{Bourbaki}(2004)}]{BourbakiLieGroupsI}
\bibinfo{author}{\bibnamefont{Bourbaki}, \bibfnamefont{N.}},
  \bibinfo{year}{2004}, \emph{\bibinfo{title}{Lie Groups and Lie Algebras}},
  volume~\bibinfo{volume}{I} (\bibinfo{publisher}{Springer}).

\bibitem[{\citenamefont{Cartier}(2007)}]{CartierHopfPrimer}
\bibinfo{author}{\bibnamefont{Cartier}, \bibfnamefont{P.}},
  \bibinfo{year}{2007}, in \emph{\bibinfo{booktitle}{Frontiers in Number
  Theory, Physics, and Geometry II}} (\bibinfo{publisher}{Springer},
  \bibinfo{address}{Berlin}), pp. \bibinfo{pages}{537--615}.

\bibitem[{\citenamefont{Coecke}(2009)}]{Coecke2009}
\bibinfo{author}{\bibnamefont{Coecke}, \bibfnamefont{B.}},
  \bibinfo{year}{2009}, \bibinfo{journal}{Contemp. Phys.}
  \textbf{\bibinfo{volume}{6}}, \bibinfo{pages}{(to appear)}.

\bibitem[{\citenamefont{Connes and Kreimer}(1998)}]{ConnesKreimer1998}
\bibinfo{author}{\bibnamefont{Connes}, \bibfnamefont{A.}}, and
  \bibinfo{author}{\bibfnamefont{D.}~\bibnamefont{Kreimer}},
  \bibinfo{year}{1998}, \bibinfo{journal}{Commun. Math. Phys.}
  \textbf{\bibinfo{volume}{199}}, \bibinfo{pages}{203}.

\bibitem[{\citenamefont{Diestel}(2005)}]{DiestelBook}
\bibinfo{author}{\bibnamefont{Diestel}, \bibfnamefont{R.}},
  \bibinfo{year}{2005}, \emph{\bibinfo{title}{Graph Theory}}
  (\bibinfo{publisher}{Springer-Verlag}, \bibinfo{address}{Heidelberg}).

\bibitem[{\citenamefont{Dirac}(1982)}]{DiracBook}
\bibinfo{author}{\bibnamefont{Dirac}, \bibfnamefont{P.~A.~M.}},
  \bibinfo{year}{1982}, \emph{\bibinfo{title}{The {P}rinciples of {Q}uantum
  {M}echanics}} (\bibinfo{publisher}{Oxford University Press},
  \bibinfo{address}{New York}), \bibinfo{edition}{4th} edition.

\bibitem[{\citenamefont{Ebrahimi-Fard and Kreimer}(2005)}]{KreimerFard}
\bibinfo{author}{\bibnamefont{Ebrahimi-Fard}, \bibfnamefont{K.}}, and
  \bibinfo{author}{\bibfnamefont{D.}~\bibnamefont{Kreimer}},
  \bibinfo{year}{2005}, \bibinfo{journal}{J. Phys. A: Math. Gen.}
  \textbf{\bibinfo{volume}{38}}, \bibinfo{pages}{R385}.

\bibitem[{\citenamefont{Flajolet and Sedgewick}(2008)}]{FlajoletBook}
\bibinfo{author}{\bibnamefont{Flajolet}, \bibfnamefont{P.}}, and
  \bibinfo{author}{\bibfnamefont{R.}~\bibnamefont{Sedgewick}},
  \bibinfo{year}{2008}, \emph{\bibinfo{title}{Analytic Combinatorics}}
  (\bibinfo{publisher}{Cambridge University Press},
  \bibinfo{address}{Cambridge}).

\bibitem[{\citenamefont{Gilmore}(1974)}]{GilmoreBook}
\bibinfo{author}{\bibnamefont{Gilmore}, \bibfnamefont{R.}},
  \bibinfo{year}{1974}, \emph{\bibinfo{title}{Lie Groups, Lie Algebras, and
  Some of Their Applications}} (\bibinfo{publisher}{Wiley},
  \bibinfo{address}{New York}).

\bibitem[{\citenamefont{Glauber}(1963)}]{Glauber}
\bibinfo{author}{\bibnamefont{Glauber}, \bibfnamefont{R.~J.}},
  \bibinfo{year}{1963}, \bibinfo{journal}{Phys. Rev.}
  \textbf{\bibinfo{volume}{130}}, \bibinfo{pages}{2529}.

\bibitem[{\citenamefont{Hall}(2004)}]{HallBook}
\bibinfo{author}{\bibnamefont{Hall}, \bibfnamefont{B.~C.}},
  \bibinfo{year}{2004}, \emph{\bibinfo{title}{Lie Groups, Lie Algebras and
  Representations: An Elementary Introduction}}
  (\bibinfo{publisher}{Springer-Verlag}, \bibinfo{address}{New York}).

\bibitem[{\citenamefont{Hughes}(1989)}]{HughesBook}
\bibinfo{author}{\bibnamefont{Hughes}, \bibfnamefont{R.~I.~G.}},
  \bibinfo{year}{1989}, \emph{\bibinfo{title}{The Structure and Interpretation
  of Quantum Mechanics}} (\bibinfo{publisher}{Harvard University Press},
  \bibinfo{address}{Harvard}).

\bibitem[{\citenamefont{Isham}(1995)}]{IshamBook}
\bibinfo{author}{\bibnamefont{Isham}, \bibfnamefont{C.~J.}},
  \bibinfo{year}{1995}, \emph{\bibinfo{title}{Lectures on {Q}uantum {T}heory:
  {M}athematical and {S}tructural {F}oundations}} (\bibinfo{publisher}{Imperial
  College Press}, \bibinfo{address}{London}).

\bibitem[{\citenamefont{Joni and Rota}(1979)}]{JoniRota}
\bibinfo{author}{\bibnamefont{Joni}, \bibfnamefont{S.~A.}}, and
  \bibinfo{author}{\bibfnamefont{G.~C.} \bibnamefont{Rota}},
  \bibinfo{year}{1979}, \bibinfo{journal}{Stud. Appl. Math.}
  \textbf{\bibinfo{volume}{61}}, \bibinfo{pages}{93}.

\bibitem[{\citenamefont{Klauder and Skagerstam}(1985)}]{Klauder}
\bibinfo{author}{\bibnamefont{Klauder}, \bibfnamefont{J.~R.}}, and
  \bibinfo{author}{\bibfnamefont{B.-S.} \bibnamefont{Skagerstam}},
  \bibinfo{year}{1985}, \emph{\bibinfo{title}{Coherent States. Application in
  Physics and Mathematical Physics}} (\bibinfo{publisher}{World Scientific},
  \bibinfo{address}{Singapore}).

\bibitem[{\citenamefont{Kreimer}(1998)}]{Kreimer1998}
\bibinfo{author}{\bibnamefont{Kreimer}, \bibfnamefont{D.}},
  \bibinfo{year}{1998}, \bibinfo{journal}{Adv. Th. Math. Phys.}
  \textbf{\bibinfo{volume}{2}}, \bibinfo{pages}{303}.

\bibitem[{\citenamefont{Kreimer}(2000)}]{KreimerBook}
\bibinfo{author}{\bibnamefont{Kreimer}, \bibfnamefont{D.}},
  \bibinfo{year}{2000}, \emph{\bibinfo{title}{Knots and Feynman Diagrams}},
  Cambridge Lecture Notes in Physics (\bibinfo{publisher}{Cambridge University
  Press}).

\bibitem[{\citenamefont{Kreimer}(2003)}]{Kreimer2003}
\bibinfo{author}{\bibnamefont{Kreimer}, \bibfnamefont{D.}},
  \bibinfo{year}{2003}, \bibinfo{journal}{Ann. Phys.}
  \textbf{\bibinfo{volume}{303}}, \bibinfo{pages}{179}.

\bibitem[{\citenamefont{Louck}(2008)}]{LouckBook}
\bibinfo{author}{\bibnamefont{Louck}, \bibfnamefont{J.~D.}},
  \bibinfo{year}{2008}, \emph{\bibinfo{title}{Unitary Symmetry And
  Combinatorics}} (\bibinfo{publisher}{World Scientific},
  \bibinfo{address}{Singapore}).

\bibitem[{\citenamefont{Marzuoli and Rasetti}(2005)}]{Rasetti}
\bibinfo{author}{\bibnamefont{Marzuoli}, \bibfnamefont{A.}}, and
  \bibinfo{author}{\bibfnamefont{M.}~\bibnamefont{Rasetti}},
  \bibinfo{year}{2005}, \bibinfo{journal}{Ann. Phys.}
  \textbf{\bibinfo{volume}{318}}, \bibinfo{pages}{345}.

\bibitem[{\citenamefont{Mattuck}(1992)}]{MattuckBook}
\bibinfo{author}{\bibnamefont{Mattuck}, \bibfnamefont{R.~D.}},
  \bibinfo{year}{1992}, \emph{\bibinfo{title}{A {G}uide to {F}eynman {D}iagrams
  in the {M}any-{B}ody {P}roblem}} (\bibinfo{publisher}{Dover Publications},
  \bibinfo{address}{New York}), \bibinfo{edition}{2nd} edition.

\bibitem[{\citenamefont{Peres}(2002)}]{PeresBook}
\bibinfo{author}{\bibnamefont{Peres}, \bibfnamefont{A.}}, \bibinfo{year}{2002},
  \emph{\bibinfo{title}{Quantum Theory: Concepts and Methods}}
  (\bibinfo{publisher}{Kluwer Academic Publishers}, \bibinfo{address}{New
  York}).

\bibitem[{\citenamefont{Schleich}(2001)}]{Schleich}
\bibinfo{author}{\bibnamefont{Schleich}, \bibfnamefont{W.~P.}},
  \bibinfo{year}{2001}, \emph{\bibinfo{title}{Quantum Optics in Phase Space}}
  (\bibinfo{publisher}{Wiley}, \bibinfo{address}{Berlin}).

\bibitem[{\citenamefont{Spekkens}(2007)}]{Spekkens}
\bibinfo{author}{\bibnamefont{Spekkens}, \bibfnamefont{R.}},
  \bibinfo{year}{2007}, \bibinfo{journal}{Phys. Rev. A}
  \textbf{\bibinfo{volume}{75}}, \bibinfo{pages}{032110}.

\bibitem[{\citenamefont{Sweedler}(1969)}]{SweedlerBook}
\bibinfo{author}{\bibnamefont{Sweedler}, \bibfnamefont{M.~E.}},
  \bibinfo{year}{1969}, \emph{\bibinfo{title}{Hopf Algebras}}
  (\bibinfo{publisher}{Benjamin}, \bibinfo{address}{New York}).

\bibitem[{\citenamefont{Wilcox}(1967)}]{Wilcox}
\bibinfo{author}{\bibnamefont{Wilcox}, \bibfnamefont{R.~M.}},
  \bibinfo{year}{1967}, \bibinfo{journal}{J. Math. Phys.}
  \textbf{\bibinfo{volume}{8}}, \bibinfo{pages}{962}.

\end{thebibliography}
