) Configurations Exist for Almost All N –– an Update
نویسنده
چکیده
It has been known since the late 1800’s that connected (n3) configurations exist if an only if n ≥ 9. However, the analogous question concerning connected (n4) configurations was not considered till very recently ([2], [3]). This is probably due to the fact that –– except for one paper early in the 20 century [5], there has been no mention in the literature of (n4) configurations till 1990 ([4]). In [3] it was shown that connected (n4) configurations exist for all n ≥ 21, with the possible exception of certain 32 values of n, the largest of which is n = 179. Since then, it was established that (n4) configurations exist for more than half of these values, and the aim of the present note is to prove the following:
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