Talk:Stars and bars (combinatorics)

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The example is incomplete

The example states that the stars and bar notation would represent the 4-tuple (1,3,0,1), but there is no way to map this to the set { a, b, c, d } unless by specifying an ordering to the set, like the 4-tuple (a,b,c,d). Am I right ? —Preceding unsigned comment added by 193.57.67.241 (talk) 10:18, 26 April 2011 (UTC)[reply]

You are right that the bijection depends on a chosen ordering of the set. But since this is about counting only, it suffices to show the existence of a bijection, not its uniqueness in any sense. So one can start by choosing an arbitrary ordering on the set, and then define the bijection in terms of that, which is what the starts and bars argument does. Often enumerative combinatorialists assume sets to be ordered without even mentioning so. Marc van Leeuwen (talk) 17:13, 26 April 2011 (UTC)[reply]

Thank you. So assuming that the chosen ordering is the one that the set has been presented with (in this case, a, then b, then c, then d), OK. I understand that there actually are 24 possible orderings yielding 12 different sets. Do you think it would be worth mentioning? —Preceding unsigned comment added by 193.57.67.241 (talk) 07:50, 27 April 2011 (UTC)[reply]