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Zs. Baranyai, On the factorization of the complete uniform hypergraph. In Infinite and finite sets
1975
Earlier work this paper cites.
G.B. Folland, Real analysis
1999
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A. Razborov, Flag algebras, J. Symbolic Logic
2007
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A. Razborov, On the minimal density of triangles in graphs, Combinatorics, Probability and Computing
2008
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José Trashorras, Large Deviations for Symmetrised Empirical Measures, Theor. Probab
2008
Earlier work this paper cites.
S. Starr, Thermodynamic limit for the Mallows model on S n S_{n} , J. Math. Phys
2009
Earlier work this paper cites.
G. Brightwell and N. Georgiou, Continuum limits for classical sequential growth models, Rand. Struc. Algor
2010
Earlier work this paper cites.
N. Madras and H. Liu, Random pattern-avoiding permutations. In Algorithmic Probability and Combinatorics
2010
Earlier work this paper cites.
C.B. Presutti and W.R. Stromquist, Packing rates of measures and a conjecture for the packing density of 2413, London Math. Soc
2010
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S. Chatterjee and S.R.S. Varadhan, The large deviation principle for the Erdős-Rényi random graph, Eur. J. Combin
2011
Earlier work this paper cites.
C. Hoppen, Y. Kohayakawa, C.G. Moreira and R.M. Sampaio, Limits of permutation sequences through permutation regularity, Arxiv:1106.1663v1 (8 Jun 2011)
Original
2011
Earlier work this paper cites.
S. Janson, Poset limits and exchangeable random posets, Combinatorica
2011
Earlier work this paper cites.

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S. Kitaev, Patterns in Permutations and Words, Springer, Berlin, 2011
2011
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L. Lovász, Large Networks and Graph Limits
2012
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D. Bevan, Growth rates of permutation grid classes, tours on graphs, and the spectral radius, ArXiv:1302.2037v4 (22 Oct 2013)
Original
2013
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S. Chatterjee and P. Diaconis, Estimating and understanding exponential random graph models, Ann. Stat
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2013
Cited alongside, same era.

Then

T. Dokos and I. Pak, The expected shape of random doubly alternating Baxter permutations, ArXiv:1401.0770, (4 Jan 2014)
Original
2014
Later among the works it cites.
R. Kenyon, C. Radin, K. Ren and L. Sadun, Multipodal structure and phase transitions in large constrained graphs, ArXiv:1405.0599v2 (9 Sep 2014)
Original
2014
Later among the works it cites.
N. Madras and L. Pehlivan. Structure of random 312-avoiding permutations, ArXiv:1401.6230v2 (9 Nov 2014). 2014
Original
2014
Later among the works it cites.
S. Minor and I. Pak, The shape of random pattern-avoiding permutations, Adv. Appl. Math
2014
Later among the works it cites.
C. Radin, K. Ren and L. Sadun, The asymptotics of large constrained graphs, J. Phys. A: Math. Theor
2014

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2015

Permutations with fixed pattern densities

Kenyon, Richard, Kral, Daniel, Radin, Charles et al.

Understand

We study scaling limits of random permutations ("permutons") constrained by having fixed densities of a finite number of patterns.

We show that the limit shapes are determined by maximizing entropy over permutons with those constraints.
In particular, we compute (exactly or numerically) the limit shapes with fixed \hbox{12} density, with fixed \hbox{12} and \hbox{123} densities, with fixed \hbox{12} density and the sum of \hbox{123} and \hbox{213} densities, and with fixed \hbox{123} and \hbox{321} densities.
In the last case we explore a particular phase transition.

Built on

Zs. Baranyai, On the factorization of the complete uniform hypergraph. In Infinite and finite sets
1975
Earlier work this paper cites.
G.B. Folland, Real analysis
1999
Earlier work this paper cites.
A. Razborov, Flag algebras, J. Symbolic Logic
2007
Earlier work this paper cites.
A. Razborov, On the minimal density of triangles in graphs, Combinatorics, Probability and Computing
2008
Earlier work this paper cites.
José Trashorras, Large Deviations for Symmetrised Empirical Measures, Theor. Probab
2008
Earlier work this paper cites.
S. Starr, Thermodynamic limit for the Mallows model on S n S_{n} , J. Math. Phys
2009
Earlier work this paper cites.
G. Brightwell and N. Georgiou, Continuum limits for classical sequential growth models, Rand. Struc. Algor
2010
Earlier work this paper cites.
N. Madras and H. Liu, Random pattern-avoiding permutations. In Algorithmic Probability and Combinatorics
2010
Earlier work this paper cites.
C.B. Presutti and W.R. Stromquist, Packing rates of measures and a conjecture for the packing density of 2413, London Math. Soc
2010
Earlier work this paper cites.
S. Chatterjee and S.R.S. Varadhan, The large deviation principle for the Erdős-Rényi random graph, Eur. J. Combin
2011
Earlier work this paper cites.
C. Hoppen, Y. Kohayakawa, C.G. Moreira and R.M. Sampaio, Limits of permutation sequences through permutation regularity, Arxiv:1106.1663v1 (8 Jun 2011)
Original
2011
Earlier work this paper cites.
S. Janson, Poset limits and exchangeable random posets, Combinatorica
2011
Earlier work this paper cites.

Similar

S. Kitaev, Patterns in Permutations and Words, Springer, Berlin, 2011
2011
Cited alongside, same era.
L. Lovász, Large Networks and Graph Limits
2012
Cited alongside, same era.
D. Bevan, Growth rates of permutation grid classes, tours on graphs, and the spectral radius, ArXiv:1302.2037v4 (22 Oct 2013)
Original
2013
Cited alongside, same era.
S. Chatterjee and P. Diaconis, Estimating and understanding exponential random graph models, Ann. Stat
2013
Cited alongside, same era.
J. Hladký, A. Máthé, V. Patel and O. Pikhurko, Poset limits can be totally ordered, ArXiv:1211.2473v2 (4 Nov 2013)
Original
2013
Cited alongside, same era.

Then

T. Dokos and I. Pak, The expected shape of random doubly alternating Baxter permutations, ArXiv:1401.0770, (4 Jan 2014)
Original
2014
Later among the works it cites.
R. Kenyon, C. Radin, K. Ren and L. Sadun, Multipodal structure and phase transitions in large constrained graphs, ArXiv:1405.0599v2 (9 Sep 2014)
Original
2014
Later among the works it cites.
N. Madras and L. Pehlivan. Structure of random 312-avoiding permutations, ArXiv:1401.6230v2 (9 Nov 2014). 2014
Original
2014
Later among the works it cites.
S. Minor and I. Pak, The shape of random pattern-avoiding permutations, Adv. Appl. Math
2014
Later among the works it cites.
C. Radin, K. Ren and L. Sadun, The asymptotics of large constrained graphs, J. Phys. A: Math. Theor
2014

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

C. Hoppen, Y. Kohayakawa, C.G. Moreira, B. Ráth and R.M. Sampaio, Limits of permutation sequences, J. Combin. Theory B

2013

Cited alongside, same era.

H. Huang, N. Linial, H. Naves, Y. Peled, and B. Sudakov, On the densities of cliques and independent sets in graphs, ArXiv:1211.4532v2 (8 Dec 2013)

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2013

Cited alongside, same era.

H. Huang, N. Linial, H. Naves, Y. Peled, and B. Sudakov, On the 3-local profiles of graphs, ArXiv:1211.3106v2 (8 Dec 2013)

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2013

Cited alongside, same era.

D. Král’ and O. Pikhurko, Quasirandom permutations are characterized by 4-point densities, Geom. Funct. Anal

2013

Cited alongside, same era.

R. Radin and L. Sadun, Phase transitions in a complex network, J. Phys. A: Math. Theor

2013

Cited alongside, same era.

M. Atapour and N. Madras, Large deviations and ratio limit theorems for pattern-avoiding permutations, Combin. Probab. Comput

2014

Cited alongside, same era.

N. Bhatnagar, and R. Peled, Lengths of monotone subsequences in a Mallows permutation, ArXiv:1306.3674v2 (21 Mar 2014)

Original

2014

Cited alongside, same era.

Later among the works it cites.

D. Bevan, Permutations avoiding 1324 and patterns in Lukasiewicz paths, ArXiv:1406.2890v2 (8 Jan 2015)

Original

2015

Closest in time.

S. Elizalde and M. Noy, The regions obtained by pairs of densities of patterns of length 3, preprint, 2015

2015

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R. Glebov, A. Grzesik, T. Klimošová and D. Král’, Finitely forcible graphons and permutons, J. Comb. Thy B

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C. Hoffman, D. Rizzolo and E. Slivken, Pattern avoiding permutations and Brownian excursion, ArXiv:1406.5156v2 (12 Jun 2015)

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2015

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S. Mukherjee, Estimation in exponential families on permutations, Arxiv: 1307.0978v3 (13 May 2015)

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R. Radin and L. Sadun, Singularities in the entropy of asymptotically large simple graphs, J. Stat. Phys

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