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Jack of all trades, master of none. Except maybe MediaWiki.

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Oct
16
comment How many ways to merge N companies into one big company: Bell or Catalan?
Interesting, but Brian M. Scott's answer, particularly the parallel to phylogenetic trees, seems more convincing. Can you spot a flaw in his argument... or in yours?
Oct
15
comment How many ways to merge N companies into one big company: Bell or Catalan?
As stated in the question, you need to substract one, because you're starting from one of the possible states.
Oct
15
comment How many ways to merge N companies into one big company: Bell or Catalan?
Presumably the intention is that each step has to merge at least one company with another, and that once merged companies can no longer be broken up.
Oct
15
comment How many ways to merge N companies into one big company: Bell or Catalan?
Yes, my understanding is that you can take multiple steps, and you can merge as many as you like (including all) in a single step. So for N=3, the valid ways to merge them would be A,B,C -> (AB,C | AC,B | BC,A) -> ABC plus A,B,C -> ABC, for a total of 4 paths.