, Volume 23, Issue 1, pp 89–95 | Cite as

The Gold Partition Conjecture

  • Marcin Peczarski


We present the Gold Partition Conjecture which immediately implies the \(1/3\)\(2/3\) Conjecture and tight upper bound for sorting. We prove the Gold Partition Conjecture for posets of width two, semiorders and posets containing at most \(11\) elements. We prove that the fraction of partial orders on an \(n\)-element set satisfying our conjecture converges to \(1\) when \(n\) approaches infinity. We discuss properties of a hypothetical counterexample.

Key words

poset linear extension \(1/3\)\(2/3\) conjecture 


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Copyright information

© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  1. 1.Institute of InformaticsWarsaw UniversityWarszawaPoland

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