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Omni-MATH / An (n, k) minus{} tournament is a contest with n players held in k rounds such that: (i) Each player plays in each round, and every two players meet at most once. (ii) If player A…

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problem

An $ (n, k) \minus{}$ tournament is a contest with n n players held in k k rounds such that: (i) (i) Each player plays in each round, and every two players meet at most once. (ii) (ii) If player A A meets player B B in round i i, player C C meets player D D in round i i, and player A A meets player C C in round j j, then player B B meets player D D in round j j. Determine all pairs (n,k) (n, k) for which there exists an $ (n, k) \minus{}$ tournament. [i]
Plain-text mathematical notation (without MathML)
An $ (n, k) \minus{}$ tournament is a contest with n players held in k rounds such that:

(i) Each player plays in each round, and every two players meet at most once.
(ii) If player A meets player B in round i, player C meets player D in round i, and player A meets player C in round j, then player B meets player D in round j.

Determine all pairs (n,k) for which there exists an $ (n, k) \minus{}$ tournament.

[i]
Original LaTeX notation
An $ (n, k) \minus{}$ tournament is a contest with $ n$ players held in $ k$ rounds such that:

$ (i)$ Each player plays in each round, and every two players meet at most once.
$ (ii)$ If player $ A$ meets player $ B$ in round $ i$, player $ C$ meets player $ D$ in round $ i$, and player $ A$ meets player $ C$ in round $ j$, then player $ B$ meets player $ D$ in round $ j$.

Determine all pairs $ (n, k)$ for which there exists an $ (n, k) \minus{}$ tournament.

[i]

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Source and history

task_id
526a5339-143e-5e60-8435-98841c6a56e9
task_key
test--526a5339-143e-5e60-8435-98841c6a56e9
task_revision_id
1
config / split
/ test

Official source

initial import