ordered positions (OrderedPosition?)

*To*: mathgroup at smc.vnet.net*Subject*: [mg83397] ordered positions (OrderedPosition?)*From*: Christian Chong-White <christian_chongwhite at hotmail.com>*Date*: Mon, 19 Nov 2007 06:18:08 -0500 (EST)

Hi Folks I am wanting an elegant solution to find an ordering of elements of a set of nested lists at a specific level (the base level in this case but need not be). The output I am after is an ordered set of positions that references each of those elements in the original structure. To explain: My ugly work-around was to flatten the nested list to get the ordering but this loses the structural information. In[22]:= Ordering[ Flatten@{{4, 3, 3, 5, 1, 2, 5, 2, 3, 2}, {1, 5, 4, 1, 3, 4, 1, 7, 3, 4}}] Out[22]= {5, 11, 14, 17, 6, 8, 10, 2, 3, 9, 15, 19, 1, 13, 16, 20, 4, 7, 12, 18} The problem with the above is I have lost the information where in the structure the element was. I need the functionality of Position - including reference to depth, and Ordering. Taking the above example further, what I am after is something like: {{1,5},{2,1}, etc} representing sorted positions of the original structure rather than {5,11, etc} of the flattened list. It seems a very "Mathematica thing" I am after, and something that could well fit within an enhanced version of Ordering, but am lost at how to address the problem in a "Mathematica elegant manner." Cheers Christian