A note on random k-dimensional posets |
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| Institution: | 1. Universidade Federal do Ceará, Fortaleza, Brazil;2. Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil;3. Universidade de São Paulo, São Paulo, Brazil;1. Dept. Computação, Universidade Federal do Ceará, Fortaleza, Brazil;2. Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil;1. Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil;2. Universidade Federal do Ceará, Fortaleza, Brazil;1. Instituto de Computação, Universidade Federal Fluminense, Niterói, RJ, Brazil;2. Instituto de Matemática, Universidade Federal do Rio de Janeiro, RJ, Brazil;3. Institute of Optimization and Operations Research, Ulm University, Germany |
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| Abstract: | In 2009, Janson Poset limits and exchangeable random posets, Institut Mittag-Leffler preprint, 36pp, arXiv:0902.0306] extended the recent theory of graph limits to posets, defining convergence for poset sequences and proving that every such sequence has a limit object. In this paper, we focus on k-dimensional poset sequences. This restriction leads to shorter proofs and to a more intuitive limit object. As before, the limit object can be used as a model for random posets, which generalizes the well known random k-dimensional poset model. This investigation also leads to a definition of quasirandomness for k-dimensional posets, which can be captured by a natural distance that measures the discrepancy of a k-dimensional poset. |
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