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Weaddressthemeanderproblem\enumeratealltopologicallyinequivalentcongurations ofa closednonselntersectingplane curveintersecting a givenline throughaxed number ofpoints". We showthatmeandersmaybe viewedasthe congurationsofasuitablefully-packedloopstatistical model dened on a random surface. Using standard results relating critical singularities of a lattice modeltoits gravitationalversiononrandomsurfaces,we predictthe meandercongurationexponent =(29+ p 145)=12 and many other meandric exponents.

From fully-packed loops to meanders, exact exponents