The Twelvefold Way

The Twelvefold Way#

  • three variables:

    • labelling of balls

    • labelling of boxes

    • at most 1 ball, at least one ball, or any number of balls

  • problems conceptually in a 2 2 3 array

  • richard stanley and that other guy

  • twelvefold table, partially filled in with already seen problems

  • we’re going to explore the rest of the problems, and enumerate possibilities for each

Implementing the Twelvefold Way#

  • for each function, we can either have ball → box mappings, or box → ball mappings, or both!

  • for more information

    • sudley place for nars2000 apl stuff

    • taocp4a for imperative generation algorithms - we’re doing recursive implementations

  • permutation function from aplcart

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