Landaus Theorem Revisited
SOUTH CAROLINA UNIV COLUMBIA COLUMBIA
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Two new elementary proofs are given of Landaus Theorem on necessary and sufficient conditions for a sequence of integers to be the score sequence for some tournament. The first is related to existing proofs by majorization, but it avoids depending on any facts about majorization. The second is natural and direct, but a bit more basic than existing proofs. Both proofs are constructive, so they each provide an algorithm for obtaining a tournament realizing a sequence satisfying Landaus conditions.
- Theoretical Mathematics