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Is there a name for permutations that have to follow a certain order?

For example, suppose ABC is a set of characters, and you are trying to figure out all the possible permutations, except, in every instance, A must be ordered before B. So thatABC ACB CAB are valid, while something like BAC would be invalid.

Matt
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    I’m not sure if there is a name for it as permutations, but it can be seen as “linear extensions of partially ordered sets.” In your case, the partial order has $A\leq A,B\leq B, C\leq C,$ and $A\leq B.$ https://en.wikipedia.org/wiki/Partially_ordered_set – Thomas Andrews Apr 16 '21 at 23:15
  • Would that be the permutation, divided by the permutations of the relevant elements? I think it is just a quotient of permutations. – RobertTheTutor Apr 16 '21 at 23:17
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    It’s definitely a subset of permutations, not a quotient, as groups. @RobertTheTutor – Thomas Andrews Apr 16 '21 at 23:19
  • Another link: https://en.wikipedia.org/wiki/Linear_extension – Thomas Andrews Apr 16 '21 at 23:22
  • True, I was thinking of counting the permutations rather than listing them. – RobertTheTutor Apr 16 '21 at 23:22
  • @ThomasAndrews Is there a formula for listing or counting partially ordered sets? Essentially treating them like permutations with some constraints? – Matt Apr 19 '21 at 11:39

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