By A. Jaffe (Chief Editor)

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Selecta Math. Sov. 11, 117-144 (1992) 6. Di Francesco, E, Golinelli, O. : Meander, folding and arch statistics. J. Math. and Computer Modelling 144, (1996) 7. : Strings, Matrix Models and Meanders. Proceedings of the 29th Inter. , Germany (1995) 8. : Contributions ~tl'rtude du probl6me des timbres poste. Canad. J. Math. 2, 385-398 (1950) 9. : A map-folding problem. Math. of Computation 22, 193-199 (1968) 10. Temperley, H. : Relations between the percolation and coloring problem and other graphtheoretical problems associated with regular planar lattices: some exact results for the percolation problem.

44) Wa,b+~ _ 1 Wa-o,b irrespectively of which term survives. 29). Similarly, if a has a minimum at i, one easily checks that the sufficient conditions 36 P. Di Francesco, O. Golinelli, E. 45) are fulfilled. Note also that wa,a = 1 as required. b= 0 3 5678 12 Fig. 21. An example of computation of wa,b, for a C b. b is obtained from a by six box additions. The box weights are computed using the rules (i)-(ii)-(iii). Here we have wa,b = (l~ll~z)3/z. 43) can be computed as a product of box factors over all the boxes which must be added to a to build b.

39) in the case k = 3,1 = 1. 7) gives an analogous relation in the case k = 3,1 = 2. 5) is orthogonal to all the elements of TLn(q = 2 cos 7r/(n + 1)), as a consequence of the identities e~ q0~n) = 0 for i = 1 , 2 , . . 8) This permits to express the last line of Gn(q = 2 cos 7r/(n + 1)) (corresponding to the diagram },V~'~) or equivalently to the element (w~n))l = 1) as a linear combination of the (Ca - 1) other lines, corresponding to diagrams with heights < (n - 1), and middle height (n - 2).

### Communications in Mathematical Physics - Volume 186 by A. Jaffe (Chief Editor)

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