---------------------------Excerpt from message dated June 12, 2001 From: U.G.Grimm@open.ac.uk To: zeilberg@euclid.math.rutgers.edu Dear Doron, it seems I now got a small problem with the definition of Brinkhuis pairs in your paper. Please have a look at this example of length 32: U_0 = 01210212010210120102012021201210 V_0 = 01210201021201210120212010201210 U_1 = 12021020121021201210120102012021 V_1 = 12021012102012021201020121012021 U_2 = 20102101202102012021201210120102 V_2 = 20102120210120102012101202120102 I believe that if fulfils your criteria on square-freeness of pairs and on the heads and tails of the words. However, it does not map square-free words onto square-free words - for instance, the word V_0 V_1 V_0 contains a square of a word of length 27: V_0 V_1 V_0 = 01210201021201210 120212010201210120210121020 120212010201210120210121020 1021201210120212010201210 With best regards, Uwe ++++++++++++++++++++++++++++++++++++++++++++ Uwe Grimm Applied Mathematics Department Mathematics & Computing Faculty The Open University Walton Hall Milton Keynes MK7 6AA U.K. Telephone: +44 1908 659991 Fax: +44 1908 652140 Email: u.g.grimm@open.ac.uk WWW: http://mcs.open.ac.uk/ugg2 ++++++++++++++++++++++++++++++++++++++++++++ ---------------------------------End excerpt