Subscription

ProductPrice 2013
MathEduc Web€ 455
MathEduc Print€ 295
more...

Help on query formulation
The Josefus permutation. (Om Josefus’ permutation.) (Danish)
Normat. Nord. Mat. Tidskr. 55, No. 1, 25-36 (2007).
Summary: It is well-known that any permutation can be presented as a composition of cycles. In fact every permutation has a unique representation, up to order, as a product of disjoint (and hence commuting) cycles. It turns out that the composition \$c_n,c_{n-1},\dots,c_2\$ where \$c_k = (1, 2, 3, \dots, k)\$ has a nice and easily found such representation, but surprisingly if the order of the cycles is reversed the problem becomes almost intractable. The elementary nature of the problem gives a good exposure to students, and it has in fact been studied by students over the years. The article is in the nature of a progress report, and the cases of \$n = 2^m, 2m-1\$ are treated in detail. Surprising connections to other parts of combinatorics are highlighted.
Classification: K20 N70