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Diary, April 1995


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Wednesday, April 5, 1995

The last weeks I have been busy with writing a program that can determine the recurrence equations for the number of Hamilton cycles in the graphs Pn x Pi, where n is fixed, and i is the parameter of the recurrence equation.

Yesterday, my program found a solution for P7 x Pi, which is: C(2i + 1) = 0, C(2) = 1, C(4) = 92, C(6) = 5320, C(8) = 301384, C(10) = 17066492, C(12) = 966656134, C(14) = 54756073582, C(16) = 3101696069920, C(18) = 175698206778318, C(20) = 9952578156814524, C(22) = 563772503196695338, C(24) = 31935387285412942410, C(26) = 1809007988782552388490, C(28) = 102472842263117124008066, C(30) = 5804663918990466729365476, C(32) = 328810272735298761062754308, C(34) = 18625745945872429428768223714, C(36) = 1055071695766249759732087999456, and C(i) = 85C(i-2) - 1932C(i-4) + 20403C(i-6) - 116734C(i-8) + 386724C(i-10) - 815141C(i-12) + 1251439C(i-14) - 1690670C(i-16) + 2681994C(i-18) - 4008954C(n-20) + 3390877C(i-22) - 1036420C(i-24) - 178842C(i-26) + 92790C(i-28) + 17732C(n-30) - 5972C(i-32) + 1728C(i-34) + 144C(i-36).

If you do not understand it, don't worry, it is probably my problem, in not explaining it clear enough.

Paris

Tomorrow, Li-Xia, my mother-in-law and I will go to Paris for two days. None of us has been there before, so we do not know what to expect. For my mother-in-law it might be the last opportunity to visit Paris, because she will go home to Urumqi in China on the 17th.


Monday, April 24, 1995

The following is something I wrote some months ago, when writing some report on concepts to be used in our research project. I had worked on it for the whole day and evening, when I wrote this:


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