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- W4380876988 abstract "The score sequence of a tournament is the sequence of the out-degrees of its vertices arranged in nondecreasing order. The problem of counting score sequences of a tournament with $n$ vertices is more than 100 years old (MacMahon 1920). In 2013 Hanna conjectured a surprising and elegant recursion for these numbers. We settle this conjecture in the affirmative by showing that it is a corollary to our main theorem, which is a factorization of the generating function for score sequences with a distinguished index. We also derive a closed formula and a quadratic time algorithm for counting score sequences." @default.
- W4380876988 created "2023-06-17" @default.
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- W4380876988 date "2023-01-01" @default.
- W4380876988 modified "2023-10-18" @default.
- W4380876988 title "Counting tournament score sequences" @default.
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- W4380876988 doi "https://doi.org/10.5817/cz.muni.eurocomb23-040" @default.
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