The size of the maximum antichains in products of linear orders

• Denis Bouyssou ^[1] ; Thierry Marchant ^[2] ; Marc Pirlot ^[3]
  1. [1] Paris Dauphine University

     Paris Dauphine University

     París, Francia

     
  2. [2] Ghent University

     Ghent University

     Arrondissement Gent, Bélgica

     
  3. [3] University of Mons

     University of Mons

     Arrondissement de Mons, Bélgica

     

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• Localización: Top, ISSN-e 1863-8279, ISSN 1134-5764, Vol. 29, Nº. 3, 2021, págs. 648-659
• Idioma: inglés
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• Resumen

  • 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.