Find words common across multiple string cells

I have a cell array where each cell has a string of different length, and each string is essentially a column of single words. Something like this

words{1,1} = ["sphere";"geometry";"number";"algebra";"function"];
words{1,2} = ["geometry";"equation";"nonlinear";"partial";"function"];
words{1,3} = ["number";"derivative";"function";"topology";"equation";"theory"];
words{1,4} = ["equation";"integral";"geometry";"function";"singular"];

I want to find words which are repeated at least once in a specified number of cells. That is, if I say words common in at least 4 cells, then I should get back

common_words = "function";

If I want words common in at least 3 cells, I should get back

common_words = ["geometry";"function";"equation"];

I can use intersect in a loop (however inefficient that might be) if the words are required to be common in all the cells. However, how do I go about finding intersections of a specific number of cells? As per my understanding, that would require combinations, and it would increase computation time exponentially with increasing cells. Is there an efficient way to do this or would I have to take combinations?

[Stephen23]

Are the words within each string vector unique?

[Tejas]

No. They can repeat within the string vector, which is why I mention a repetition of at least once in different cells.

[Stephen23]

Is the cell array or are the strings particularly large? Would there be any memory issues if they were concatenated or merged together?

[Tejas]

There are 40 cells in the array, and the largest string vector is 3238x1. I can also reduce this by removing repeated words within a string vector, but I think the maximum length goes to about 3000. The mean string length across all cells is in fact around 2000, since initial cells have smaller string vectors. If it helps, I've attached the file containing these strings.

Answer 1

[Stephen23]

My ancient version does not support strings, so I used cell arrays of character vectors, but I would expect that this should work for string as well. Approach: get unique words, concatenate, count using a histogram function:

words{1,1} = {'sphere';'geometry';'number';'algebra';'function'};
words{1,2} = {'geometry';'equation';'nonlinear';'partial';'function'};
words{1,3} = {'number';'derivative';'function';'topology';'equation';'theory'};
words{1,4} = {'equation';'integral';'geometry';'function';'singular'};

tmp = cellfun(@unique,words,'uni',0);
tmp = vertcat(tmp{:});
[uni,~,idx] = unique(tmp);
cnt = histc(idx,1:max(idx));
out = uni(cnt>=3)

Or as a function:

>> fun = @(n) uni(cnt>=n);
>> fun(4)
ans = 
    'function'
>> fun(3)
ans = 
    'equation'
    'function'
    'geometry'

[Tejas]

This works for me! Thank you.