what do you call this re-ordering operation on a list?
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From: lloyd on 2 Jul 2010 16:21 Given a list, what do you call the reordering operation that you get by stepping through the elements of a list n positions at a time, considering the list to wrap around? For instance, here's my list, L=[a,b,c,d,e,f]. I'll call the operation Q_n, where n is the number of positions to move at a time. Q_1(L) = L = [a,b,c,d,e,f,g] Q_2(L) = [a,c,e,g,b,d,f] Q_3(L) = [a,d,g,c,f,b,e] etc. Obviously the operation is only defined if n is coprime to the length of the list. Surely there is a name for this kind of operation? What would you call it?
From: Bill Dubuque on 2 Jul 2010 16:56 lloyd <lloyd.houghton(a)gmail.com> writes: > Given a list, what do you call the reordering operation that you get > by stepping through the elements of a list n positions at a time, > considering the list to wrap around? > > For instance, here's my list, L=[a,b,c,d,e,f]. I'll call the operation > Q_n, where n is the number of positions to move at a time. > > Q_1(L) = L = [a,b,c,d,e,f,g] > Q_2(L) = [a,c,e,g,b,d,f] > Q_3(L) = [a,d,g,c,f,b,e] > > etc. Obviously the operation is only defined if n is coprime to the > length of the list. Surely there is a name for this kind of operation? > What would you call it? Q_j is just a multiplication permutation (mod 7), i.e. i -> ij I doubt there's any widely recognized more concise name for such.
From: George Jefferson on 2 Jul 2010 18:03 "lloyd" <lloyd.houghton(a)gmail.com> wrote in message news:b33f7e42-6979-4bbd-96eb-bad71ec0957e(a)j8g2000yqd.googlegroups.com... > Given a list, what do you call the reordering operation that you get > by stepping through the elements of a list n positions at a time, > considering the list to wrap around? > > For instance, here's my list, L=[a,b,c,d,e,f]. I'll call the operation > Q_n, where n is the number of positions to move at a time. > > Q_1(L) = L = [a,b,c,d,e,f,g] > Q_2(L) = [a,c,e,g,b,d,f] > Q_3(L) = [a,d,g,c,f,b,e] > > etc. Obviously the operation is only defined if n is coprime to the > length of the list. Surely there is a name for this kind of operation? > What would you call it? Modular arithmetic? The ith index is simply n*i mod #L. It's nothing special and generally doesn't have any useful purpose compared to the main arragements of a list(sorted, unsorted, ascending, descending, etc...). n does't have to be coprime but one will simply get a subset of L.
From: James Waldby on 3 Jul 2010 01:37
On Fri, 02 Jul 2010 13:21:46 -0700, lloyd wrote: > Given a list, what do you call the reordering operation that you get by > stepping through the elements of a list n positions at a time, > considering the list to wrap around? > > For instance, here's my list, L=[a,b,c,d,e,f]. I'll call the operation > Q_n, where n is the number of positions to move at a time. > > Q_1(L) = L = [a,b,c,d,e,f,g] > Q_2(L) = [a,c,e,g,b,d,f] > Q_3(L) = [a,d,g,c,f,b,e] > But your list L has no g in it. > etc. Obviously the operation is only defined if n is coprime to the > length of the list. Surely there is a name for this kind of operation? > What would you call it? Like Bill said, a multiplication permutation, or as George said, modular arithmetic. However, if items were removed when selected, it would be the Josephus problem or Josephus permutation. See <http://en.wikipedia.org/wiki/Josephus_problem> -- jiw |