The size of the maximum antichains in products of linear orders

Denis Bouyssou, Thierry Marchant and Marc Pirlot ()
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Marc Pirlot: Université de Mons

TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, 2021, vol. 29, issue 3, No 3, 648-659

Abstract: Abstract The size of maximum antichains in the product of n linear orders is known when the n linear orders have the same length. We present an exact expression for the size of maximum antichains when the linear orders have (possibly) different lengths. From this, we derive an exact expression for the size of maximum antichains in the product of n linear orders with the same length. This expression is equivalent to but different from the existing expression. It allows us to present an asymptotic result for the size of maximum antichains of n linear orders with the same length m going to infinity.

Keywords: Maximal antichain; Sperner; Multichoice cooperative game; Linear orders; 91B06 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11750-020-00587-6

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