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The Gold Partition Conjecture

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Abstract

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.

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Authors and Affiliations

  1. Institute of Informatics, Warsaw University, ul. Banacha 2, 02-097, Warszawa, Poland

    Marcin Peczarski

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  1. Marcin Peczarski
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Correspondence to Marcin Peczarski.

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Peczarski, M. The Gold Partition Conjecture. Order 23, 89–95 (2006). https://doi.org/10.1007/s11083-006-9033-1

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  • DOI: https://doi.org/10.1007/s11083-006-9033-1

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