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Apr 14, 2021 at 8:03 comment added gualterio Thank you for your answer! I will study your answer.
Apr 14, 2021 at 6:41 comment added Per Alexandersson @SamHopkins Ah, right! I was too hasty.
Apr 13, 2021 at 19:12 history edited Per Alexandersson CC BY-SA 4.0
added other interpretation
Apr 13, 2021 at 19:08 comment added Sam Hopkins You're still answering the question for subsets and not tuples. The subsets question is well-known and explained for instance in Stanley's EC 2, Example 7.18.8(a) (as I had mentioned in a previous comment which I deleted after realizing the OP was interested in tuples).
Apr 13, 2021 at 19:07 comment added Per Alexandersson @PhilTosteson Yeah, I realized I had some mistakes in my code. It now agrees with the answer above.
Apr 13, 2021 at 19:05 history edited Per Alexandersson CC BY-SA 4.0
added 1572 characters in body
Apr 13, 2021 at 18:12 comment added Phil Tosteson I'm confused by this answer: first the OP seemed to want the product not the set of size $k$ subsets, and second you seem to be claiming that Sn acts trivially on size k subsets, which is false.
Apr 13, 2021 at 17:46 history answered Per Alexandersson CC BY-SA 4.0