Question

I am wondering how one can write a special Tally function, which treats the following list {{{1,0},{2,1,3}},{{1,1},{0,1,1}},{{2,1,2},{3,2}},{{1,0},{2,1}}} as if:

1. as long as dimensions match, it is equivalent. For example, {{1,0},{2,1,3}} and {{1,1},{0,1,1}} are equivalent, but not with {{1,0},{2,1}}.
2. ordering also does not matter. For example, {{1,0},{2,1,3}} and {{2,1,2},{3,2}} are equivalent.

The elements of the level 1 list can be artitarily nested. How can I write such a function?

Many thanks.

Answer 1

Very similar to @Daniel’s answer, but preserves a member of each class:

In[9]:= Tally[list, (Sort[Length /@ #] == Sort[Length /@ #2]) &]

Out[9]= {{{{1, 0}, {2, 1, 3}}, 3}, {{{1, 0}, {2, 1}}, 1}}