# Limits of permutation sequences through permutation regularity

@article{Hoppen2011LimitsOP, title={Limits of permutation sequences through permutation regularity}, author={Carlos Hoppen and Yoshiharu Kohayakawa and Carlos Gustavo Moreira and Rudini Menezes Sampaio}, journal={arXiv: Combinatorics}, year={2011} }

A permutation sequence $(\sigma_n)_{n \in \mathbb{N}}$ is said to be convergent if, for every fixed permutation $\tau$, the density of occurrences of $\tau$ in the elements of the sequence converges. We prove that such a convergent sequence has a natural limit object, namely a Lebesgue measurable function $Z:[0,1]^2 \to [0,1]$ with the additional properties that, for every fixed $x \in [0,1]$, the restriction $Z(x,\cdot)$ is a cumulative distribution function and, for every $y \in [0,1]$, the…

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