Is the gold partition conjecture true?
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The gold partition conjecture is a generalization of the 1/3–2/3 conjecture:
The gold partition conjecture states that in each partial order that is not a total order one can find two consecutive comparisons such that, if E(i) denotes the number of linear extensions remaining after i of the comparisons have been made, then E(0) ≥ E(1) + E(2). If this conjecture is true, it would imply the 1/3–2/3 conjecture.
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