---------------------------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 
++++++++++++++++++++++++++++++++++++++++++++

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