Permutations with equal orders
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Abstract Let ${\mathbb{P}}(ord\pi = ord\pi ')$ be the probability that two independent, uniformly random permutations of [n] have the same order. Answering a question of Thibault Godin, we prove that ${\mathbb{P}}(ord\pi = ord\pi ') = {n^{ - 2 + o(1)}}$ and that ${\mathbb{P}}(ord\pi = ord\pi ') \ge {1 \over 2}{n^{ - 2}}lg*n$ for infinitely many n. (Here lg*n is the height of the tallest tower of twos that is less than or equal to n.)
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2017 ◽
Vol 63
(6)
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pp. 4050-4054
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2016 ◽
Vol 52
(4)
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pp. 1614-1640
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Revue de l Institut International de Statistique / Review of the International Statistical Institute
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1963 ◽
Vol 31
(2)
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pp. 261
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2004 ◽
Vol 37
(24)
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pp. 6221-6241
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2000 ◽
Vol 17
(3-4)
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pp. 238-259
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