Ju l 2 00 5 The dinner table problem : the rectangular case
نویسنده
چکیده
Assume that 8 people are seated around a table and we want to enumerate the number of ways that they can be permuted such that neighbors are no more neighbors after the rearrangement. Of course the answer depends on the topology of the table: if the table is a circle then it is easy to check by a simple computer program that the permutations that verify this property are 2832, if it is a long bar and all the persons seat along one side then they are 5242. Furthermore, if it is a rectangular table with two sides then the rearrangements are 9512. The first two cases are respectively described by sequences A089222 and A002464 of the On-Line Encyclopedia of Integer Sequences [3], on the other hand the rectangular case does not appear in the literature. Here is a valid rearrangement for n = 8:
منابع مشابه
The Dinner Table Problem: the Rectangular Case
Consider n people who are seated randomly at a rectangular table with ⌊n/2⌋ and ⌈n/2⌉ seats along the two opposite sides, for two dinners. What is the probability that neighbors at the first dinner are no longer neighbors at the second one? We give an explicit formula and show that its asymptotic behavior as n goes to infinity is e(1+ 4/n) (it is known that it is e(1−4/n) for a round table). A ...
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