Nested list transformations

• To: mathgroup at smc.vnet.net
• Subject: [mg96872] Nested list transformations
• From: Maxim <vmu at mail.ru>
• Date: Thu, 26 Feb 2009 07:58:41 -0500 (EST)

```Hello everybody.

I was wondering if Mathematica can be helpful in the following problem.
Suppose we have a nested list:
{{1}, {2, 3}}
And we are trying to do different kinds of transformations to this list. Like this:
{{3, 1}, {2}},
{{3}, {1, 2}}
This was a one element movement from one inner list to another. Also there can be element exchanges and two several sequential element movements etc.
What I want to do is to keep track of these changes and see if some set of the transformations can lead to the list that is equal to the initial list.
I showed this simplest possible example, but actually the Depth[] of the outer list should be 4:
{
{
{1, 2, 3}, {2, 3, 4}, ...
},
{
{5, 6, 7}, {8, 5, 1}, {8, 1, 6},
},
....
}

I guess that I should use Combinatorica package for this, but I'm not sure. And I'm not sure about the mathematical theory behidn this.

```

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