- Author
- Denis Bouyssou, Thierry Marchant (UGent) and Marc Pirlot
- Organization
- 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
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8687541
- MLA
- Bouyssou, Denis, et al. “The Size of the Maximum Antichains in Products of Linear Orders.” TOP, vol. 29, 2021, pp. 648–59, doi:10.1007/s11750-020-00587-6.
- APA
- Bouyssou, D., Marchant, T., & Pirlot, M. (2021). The size of the maximum antichains in products of linear orders. TOP, 29, 648–659. https://doi.org/10.1007/s11750-020-00587-6
- Chicago author-date
- Bouyssou, Denis, Thierry Marchant, and Marc Pirlot. 2021. “The Size of the Maximum Antichains in Products of Linear Orders.” TOP 29: 648–59. https://doi.org/10.1007/s11750-020-00587-6.
- Chicago author-date (all authors)
- Bouyssou, Denis, Thierry Marchant, and Marc Pirlot. 2021. “The Size of the Maximum Antichains in Products of Linear Orders.” TOP 29: 648–659. doi:10.1007/s11750-020-00587-6.
- Vancouver
- 1.Bouyssou D, Marchant T, Pirlot M. The size of the maximum antichains in products of linear orders. TOP. 2021;29:648–59.
- IEEE
- [1]D. Bouyssou, T. Marchant, and M. Pirlot, “The size of the maximum antichains in products of linear orders,” TOP, vol. 29, pp. 648–659, 2021.
@article{8687541,
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.}},
author = {{Bouyssou, Denis and Marchant, Thierry and Pirlot, Marc}},
issn = {{1134-5764}},
journal = {{TOP}},
keywords = {{Maximal antichain,Sperner,Multichoice cooperative game,Linear orders}},
language = {{eng}},
pages = {{648--659}},
title = {{The size of the maximum antichains in products of linear orders}},
url = {{http://doi.org/10.1007/s11750-020-00587-6}},
volume = {{29}},
year = {{2021}},
}
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