Coordinating Pebble Motion On Graphs the Diameter of Permutation Groups And App
Coordinating Pebble Motion On Graphs the Diameter of Permutation Groups And App
D M Kornhauser
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We want this to be less than 3A;. So: n/k Jn/Z. This suggests that we should use at least on the order of y/n crossings to create a likely exponential puzzle. It would be of great interest to establish an exponential or moderately exponential lower bound for some of these ''candidate" puzzles. We now leave these examples and speculations, and state some results about the diameter of permutation groups (proofs in final version). 3. 2. Some results about the diameter of permutation groups The fo...llowing are classical theorems in the theory of permutation groups. Theorem A If the group G on n letters is A:-transitive and k > n/3 + 1, then G = A„ or Sn- Theorem B If G is primitive on n letters, and a subgroup // moves only m 'C n letters and is primitive on tliem, then G \s n — m + 1-transitive. We prove the following versions of these theorems, which give information about the diameter: Theorem 1 If group C on n letters is A:-transitive in words of Icngtli
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