On a question of Vera T. Sós about size forcing of graphons

Cooley, Oliver; Kang, Mihyun; Pikhurko, Oleg

doi:10.1007/s10474-022-01265-8

Acta Math. Hungar.

2022

DOI: 10.1007/s10474-022-01265-8

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On a question of Vera T. Sós about size forcing of graphons

Oliver Cooley

Mihyun Kang

Oleg Pikhurko

Abstract: How to cite:Please refer to published version for the most recent bibliographic citation information. If a published version is known of, the repository item page linked to above, will contain details on accessing it.

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2024

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Increasing subsequences of linear size in random permutations and the Robinson–Schensted tableaux of permutons

Dubach

2024

Random Struct Algorithms

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The study of longest increasing subsequences (LIS) in permutations led to that of Young diagrams via Robinson–Schensted's (RS) correspondence. In a celebrated paper, Vershik and Kerov obtained a limit theorem for such diagrams and found that the LIS of a uniform permutation of size behaves as . Independently and much later, Hoppen et al. introduced the theory of permutons as a scaling limit of permutations. In this paper, we extend in some sense the RS correspondence of permutations to the space of permutons. When the “RS‐tableaux” of a permuton are non‐trivial, we show that the RS‐tableaux of random permutations sampled from this permuton exhibit a linear behavior, in the sense that their first rows and columns have lengths of linear order. In particular, the LIS of such permutations behaves as a multiple of . We also prove some large deviation results for these convergences. Finally, by studying asymptotic properties of Fomin's algorithm for permutations, we show that the RS‐tableaux of a permuton satisfy a partial differential equation.

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Increasing subsequences of linear size in random permutations and the Robinson–Schensted tableaux of permutons

Dubach

2024

Random Struct Algorithms

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On a question of Vera T. Sós about size forcing of graphons

Abstract: How to cite:Please refer to published version for the most recent bibliographic citation information. If a published version is known of, the repository item page linked to above, will contain details on accessing it.

Cited by 1 publication

References 28 publications

Increasing subsequences of linear size in random permutations and the Robinson–Schensted tableaux of permutons

Increasing subsequences of linear size in random permutations and the Robinson–Schensted tableaux of permutons

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