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                <title xml:lang="en">Fully Packed Loop configurations in a triangle and Littlewood Richardson coefficients</title>
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                    <forename type="first">Philippe</forename>
                    <surname>Nadeau</surname>
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                <title level="j">Discrete Mathematics and Theoretical Computer Science</title>
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                  <title>22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)</title>
                  <date type="start">2010</date>
                  <settlement>San Francisco</settlement>
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                <editor>Billey</editor>
                <editor>Sara and Reiner</editor>
                <editor>Victor</editor>
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                  <publisher>Discrete Mathematics and Theoretical Computer Science</publisher>
                  <publisher>DMTCS</publisher>
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                  <biblScope unit="volume">DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)</biblScope>
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                <term xml:lang="en">Littlewood―Richardson coefficients</term>
                <term xml:lang="en">Fully Packed Loop</term>
                <term xml:lang="en">Razumov Stroganov conjecture</term>
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              <p>We are interested in Fully Packed Loops in a triangle (TFPLs), as introduced by Caselli at al. and studied by Thapper. We show that for Fully Packed Loops with a fixed link pattern (refined FPL), there exist linear recurrence relations with coefficients computed from TFPL configurations. We then give constraints and enumeration results for certain classes of TFPL configurations. For special boundary conditions, we show that TFPLs are counted by the famous Littlewood Richardson coefficients.</p>
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              <p>Nous nous intéressons aux configurations de "Fully Packed Loops'' dans un triangle (TFPL), introduites par Caselli et al. et étudiées par Thapper. Nous montrons que pour les Fully Packed Loops avec un couplage donné, il existe des relations de récurrence linéaires dont les coefficients sont calculés à partir de certains TFPLs. Nous donnons ensuite des contraintes et des résultats énumératifs pour certaines familles de TFPLs. Pour certaines conditions au bord, nous montrons que le nombre de TFPL est donné par les coefficients de Littlewood Richardson.</p>
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