A note on random k-dimensional posets

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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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The second author acknowledges the support by FAPERGS (Proc. 10/0388-2), FAPESP (Proc. 2007/56496-3), and CNPq (Proc. 484154/2010-9). The third author was partially supported by CNPq (Proc. 308509/2007-2, 484154/2010-9). The fourth author was partially supported by Funcap (Proc. 07.013.00/09) and CNPq (Proc. 484154/2010-9).

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