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\title{{\bf Deformation theory of Hopf algebras appearing in Combinatorial Physics}}

\author{G H E Duchamp$^{\dag}$, P Blasiak$^{\ddag}$, A Horzela$^\ddag$, K A Penson$^{\diamondsuit}$\\ and A I Solomon$^{\diamondsuit,\sharp}$}
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\address{\rm
$^a$ LIPN - UMR 7030\\
CNRS - Universit\'e Paris 13\\
F-93430 Villetaneuse, France}
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\address{\rm
$^\ddag$ H.Niewodnicza\'nski Institute of
Nuclear Physics, Polish Academy of Sciences\\
ul. Eliasza-Radzikowskiego 152,  PL 31342 Krak\'ow, Poland}
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\address{\rm
$^\diamondsuit$ Laboratoire de Physique Th\'eorique de la Mat\`ere Condens\'ee,\\
Universit\'e Pierre et Marie Curie, CNRS UMR 7600\\
Tour 24 - 2e \'et., 4 pl. Jussieu, F 75252 Paris Cedex 05, France}
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\address{\rm
$^{\sharp}$ The Open University, Physics and Astronomy Department\\
Milton Keynes MK7 6AA, United Kingdom}

\begin{document}
\maketitle

\begin{abstract}
The original Hopf algebra inherent to the pre-Feynman diagrams (LDIAG) of the 
Quantum Field Theory of Partitions (QFTP) admits a three-parameter deformation. 
It turns out that the two first parameters (deformation of the structure of algebra) 
are of different nature : the first is due to the deformation of the (tensor) space 
by a commutation factor and the second to a perturbation of the comultiplication. 
The very general tools for deformation are detailed (coloured products, dual laws, 
diagonal deformation, Swedler's duals). 
As a byproduct, one gets an unexpected deformation of the Euler-Zagier sums.
\end{abstract}

\end{document}