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            <title xml:lang="en">Meander Graphs</title>
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                <forename type="first">Christine E.</forename>
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            <idno type="halRefHtml">&lt;i&gt;23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)&lt;/i&gt;, 2011, Reykjavik, Iceland. pp.469-480, &lt;a target="_blank" href="https://dx.doi.org/10.46298/dmtcs.2926"&gt;&amp;#x27E8;10.46298/dmtcs.2926&amp;#x27E9;&lt;/a&gt;</idno>
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                <title xml:lang="en">Meander Graphs</title>
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                    <forename type="first">Christine E.</forename>
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                <title level="j">Discrete Mathematics and Theoretical Computer Science</title>
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                  <title>23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)</title>
                  <date type="start">2011</date>
                  <settlement>Reykjavik</settlement>
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                <editor>Bousquet-Mélou</editor>
                <editor>Mireille and Wachs</editor>
                <editor>Michelle and Hultman</editor>
                <editor>Axel</editor>
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                  <biblScope unit="volume">DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)</biblScope>
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                <term xml:lang="en">perfect matchings</term>
                <term xml:lang="en">noncrossing partitions</term>
                <term xml:lang="en">combinatorial enumeration</term>
                <term xml:lang="en">Markov chain Monte Carlo</term>
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              <p>We consider a Markov chain Monte Carlo approach to the uniform sampling of meanders. Combinatorially, a meander $M = [A:B]$ is formed by two noncrossing perfect matchings, above $A$ and below $B$ the same endpoints, which form a single closed loop. We prove that meanders are connected under appropriate pairs of balanced local moves, one operating on $A$ and the other on $B$. We also prove that the subset of meanders with a fixed $B$ is connected under a suitable local move operating on an appropriately defined meandric triple in $A$. We provide diameter bounds under such moves, tight up to a (worst case) factor of two. The mixing times of the Markov chains remain open.</p>
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              <p>Nous considérons une approche de Monte Carlo par chaîne de Markov pour l'échantillonnage uniforme des méandres. Combinatoirement, un méandre $M = [A : B]$ est constitué par deux couplages (matchings) parfaits sans intersection $A$ et $B$, définis sur le même ensemble de points alignés, et qui forment une boucle fermée simple lorsqu'on dessine $A$ "vers le haut'' et $B$ "vers le bas''. Nous montrons que les méandres sont connectés sous l'action de paires appropriées de mouvements locaux équilibrés, l'un opérant sur $A$ et l'autre sur $B$. Nous montrons également que le sous-ensemble de méandres avec un $B$ fixe est connecté sous l'action de mouvements locaux définis sur des "triplets méandriques'' de $A$. Nous fournissons des bornes sur les diamètres pour de tels mouvements, exactes à un facteur 2 près (dans le pire des cas). Les temps de mélange des chaînes de Markov demeurent une question ouverte.</p>
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