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Re: Order of Permutations of a Certain ~Kind~ Across the (Odd) Integers
Posted:
Jan 9, 2013 2:31 PM


On Tue, 08 Jan 2013 22:28:05 +0100, Timothy Murphy wrote: > P. Michael Hutchins wrote: >> A ~kind~ of permutation  call it "inside out"  can be specified for any >> integer. (I use only the odd ones, for reasons that should become >> obvious.) >> >> For a set of N elements.. >> (which I represent as just a string of integers  eg: 12345) >> >> ..the permutation takes: to: >> o the middle one (N+1/2): 1 >> o the one to the left of that: 2 >> o the one to the right of that: 3 >> ...and so on >> >> eg: for 12345, we have: >> >> 12345 >> 34251 >> 25413 >> 41532 >> 53124 >> 12345 >> >> ...so this guy's order is 5. > > I cannot follow your example. > As far as I can see from your description > 3>1, 2>2, 4>3, 1>4, 5>5, > ie (1,4,3)(2)(5) with order 3. > > I'm assuming that "that" means "the middle one", ie 3.
Hutchins' description seems to have 'left' and 'right' reversed. A tuple (1, 2, 3 ... 2m1) permutes to ( m, m+1, m1, m+2, m2, m+3 ... 2m1, 1)
 jiw



