How to generate multinomial configurations using perms, combk, ...?

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Satyajit Ghosh
Satyajit Ghosh 2018-11-27
Trying to write a function to generate all possible configurations of a state. State mean number of data points falling in each bin of histogram. For example, state (1,3,1,0,1,1,1) means first been contain 1 data, and so on. Now, evidently in the above state there are total 8 (=1+3+1+0+1+1+1) events. Let's name all 8 events like this - a,b,c,d,e,f,g,h.
Then possible configurations for the given state are -
(a)(bcd)(e)()(f)(g)(h)
(a)(bcd)(e)()(f)(h)(g)
(a)(bcd)(e)()(g)(f)(h)
.....................
.....................
Want to determine all possible configurations in computationally efficient way. I already wrote a code using a 'combnk' and complicated for loop which turned out to be very slow. Now I am thinking about using 'perms' like this -
>> perms(h,g,f,e,d,c,b,a)
But this will give me 8! configurations. But I rather want , which is nothing but multinomial coefficient. Means configurations like (a)(bcd)(e)()(f)(g)(h) and (a)(cbd)(e)()(f)(g)(h) are not different and we should have mechanism to eliminate those.

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