Abstract
Craven's conjecture says that 2n−1 is the maximum number of linear orders on {1, 2,...n} that simultaneously satisfy certain restrictions on three-element subsets of {1, 2,...n}. This is true for n=3, but the maximum exceeds 2n−1 for n≧4. There is a set of nine linear orders on {1, 2, 3, 4} that satisfy the restrictions. As n gets large, the ratio of the size of the maximum satisfying set to 2n−1 approaches infinity.
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References
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Fishburn, P. Notes on Craven's conjecture. Soc Choice Welfare 9, 259–262 (1992). https://doi.org/10.1007/BF00192881
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DOI: https://doi.org/10.1007/BF00192881