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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.
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L. Lovász and B. Szegedy, Limits of dense graph sequences, Journal of Combinatorial Theory Series B
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G. Elek, On limits of finite graphs, Combinatorica
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C. Borgs, J. T. Chayes, L. Lovász, V. T. Sós, B. Szegedy and K. Vesztergombi, Convergent sequences of dense graphs II: Multiway cuts and statistical physics, preprint
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G. Elek and B. Szegedy, Limits of hypergraphs, Removal and Regularity Lemmas. A non-standard approach, preprint
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C. Hoppen, Y. Kohayakawa, and R. M. Sampaio, A note on permutation regularity, to appear in Discrete Applied Mathematics , 14pp
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C. Hoppen, Y. Kohayakawa, C. G. Moreira and R. M. Sampaio, Testing permutation properties through subpermutations, Theoretical Computer Science 412 (29)
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G. Elek, On the limit of large girth graph sequences, Combinatorica
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C. Hoppen, Y. Kohayakawa, C. G. Moreira, B. Ráth and R. M. Sampaio, Limits of permutation sequences, preprint (2011), 21 pp
2011
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