\magnification=1200
\hsize=4in
\overfullrule=0pt
\input amssym
%\def\frac#1 #2 {{#1\over #2}}
\def\emph#1{{\it #1}}
\def\em{\it}
\nopagenumbers
\noindent
%
%
{\bf Paul Zinn-Justin}
%
%
\medskip
\noindent
%
%
{\bf Littlewood--Richardson Coefficients and Integrable Tilings}
%
%
\vskip 5mm
\noindent
%
%
%
%
We provide direct proofs of product and coproduct formulae for Schur
functions where the coefficients (Littlewood--Richardson coefficients)
are defined as counting puzzles. The product formula includes a second
alphabet for the Schur functions, allowing in particular to recover
formulae of [Molev--Sagan '99] and [Knutson--Tao '03] for factorial
Schur functions.  The method is based on the quantum integrability of
the underlying tiling model.

\bye