-2
$\begingroup$

I understand the difference between permutation and combination. But how is composition different from combination ?

Edit: I am referring to this Composition

  • 0
    What's your definition of "composition"? It's not a standard term in combinatorics (though it is in other mathematical contexts). – 2017-02-01
  • 0
    Maybe the OP means composition of permutations, though the question should be edited to make this clearer. – 2017-02-01
  • 0
    Edited my question. Please check now – 2017-02-01
  • 0
    Is it not clear to you from the link you provided ? – 2017-02-01

2 Answers 2

1

Perhaps what you are looking for is how to find the number of compositions of $n = 8,\;$ say.

Take a string of eight 1's enclosed in parentheses, (11111111)

Now place either a +, or a special symbol,$\;$ )+($\;$ between the 1's, e.g.

(1+1)+(1+1+1)+(1)+(1+1)

Since you have $2$ choices for each gap between the $1's,$ # of compositions = $2^{n-1}$

0

Compositions are permuted integer partitions. They are integer partitions with considering the order of the parts.