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Dr Michael Albert, Department of Computer Science


Meandering along


Archway 2


A meander is a non self-intersecting closed curve, which crosses a fixed line in a certain number of places. Think of a loop of rope laid on the ground, some on the carpet and some on the wood floor. Two such meanders are equivalent if you can change one into the other by rearranging the rope on the carpet, on the wood, or both, but without pulling loops across the boundary. The number of inequivalent meanders with a fixed number of crossings is of interest in certain field theories in statistical physics.

We'll introduce a combinatorial encoding of meanders as strings of symbols, and determine certain subclasses and superclasses of the resulting language of meanders. This, plus a healthy dose of good old fashioned scientific computing, is enough to determine better asymptotic bounds on meander numbers than were previously known.

Joint work with M.S. Paterson (Warwick)

Last modified: Tuesday, 03-Aug-2004 11:46:41 NZST

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