The dinner table problem: the rectangular case

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dc.creatorTauraso, Roberto
dc.date2005-07-14
dc.date.accessioned2026-07-07T05:21:42Z
dc.date.available2026-07-07T05:21:42Z
dc.description$n$ people are seated randomly at a rectangular table with $\lfloor n/2\rfloor$ and $\lceil n/2\rceil$ seats along the two opposite sides for two dinners. What's the probability that neighbors at the first dinner are no more neighbors at the second one? We give an explicit formula and we show that its asymptotic behavior as $n$ goes to infinity is $e^{-2}(1+4/n)$ (it is known that it is $e^{-2}(1-4/n)$ for a round table). A more general permutation problem is also considered.
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/math/0507293
dc.identifierhttp://arxiv.org/abs/math/0507293
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75786
dc.subjectCombinatorics
dc.subject05A05
dc.titleThe dinner table problem: the rectangular case
dc.typetext

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