Count sublists containing certain strings

Question

I have a nested list which looks like:

and I would like to count the following:

• all sublists containing {n_,n_} && {n_,n_,n_}
• all sublists containing {l_,l_} && {l_,l_,l_}
• all sublists with any combination of the above like {l_,n_} or {n_,l_,l_} or {n_,n_,l_}

in addition I would like to separate those cases when I have {l_,l_,l_} with text on it like the one highlighted. Any suggestion is really appreciated

Answer 1

You should provide copy/pastable input. Here is a random example list:

rlist := With[{len = RandomInteger[{2, 3}]},
    MapThread[Subscript, {RandomChoice[{n, l}, len], RandomInteger[10, len]}]
]

SeedRandom[1]
list = Table[rlist, 20];
list //TeXForm

$\left\{\left\{l_1,n_4,l_0\right\},\left\{l_8,l_0\right\},\left\{l_1,n_8\right\},\left\{n_{10},l_8\right\},\left\{n_8,l_5\right\},\left\{l_1,l_1,l_1\right\},\left\{n_9,l_6\right\},\left\{l_8,n_7\right\},\left\{n_8,n_0,l_9\right\},\left\{n_2,n_5,l_3\right\},\left\{n_0,n_4,n_7\right\},\left\{l_{10},l_6\right\},\left\{n_3,n_2\right\},\left\{n_3,l_9,l_5\right\},\left\{n _{10},n_1\right\},\left\{l_4,l_4\right\},\left\{n_{10},l_8\right\},\left\{n_2,n_5,n_6\right \},\left\{l_3,l_3,l_1\right\},\left\{l_0,n_{10}\right\}\right\}$

Then, you can use Tally to obtain your desired counts:

Tally[Union /@ list[[All, All, 1]]]

{{{l, n}, 11}, {{l}, 5}, {{n}, 4}}