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We consider a random permutation drawn from the set of 132-avoiding permutations of length $n$ and show that the number of occurrences of another pattern $\sigma$ has a limit distribution, after scaling by $n^{\lambda(\sigma)/2}$ where $\lambda(\sigma)$ is the length of $\sigma$ plus the number of descents.
Patrick Billingsley, Convergence of Probability Measures . Wiley, New York, 1968
1968
Earlier work this paper cites.
Richard T. Durrett, Donald L. Iglehart and Douglas R. Miller, Weak convergence to Brownian meander and Brownian excursion. Ann. Probability 5
1977
Earlier work this paper cites.
Rodica Simion and Frank W. Schmidt, Restricted permutations. European J. Combin. 6
1985
Earlier work this paper cites.
G. Louchard, The Brownian excursion area: a numerical analysis. Comput. Math. Appl. 10
1986
Earlier work this paper cites.
David Aldous, The continuum random tree II: an overview. Stochastic Analysis (Durham, 1990) , 23–70, London Math. Soc. Lecture Note Ser. 167, Cambridge Univ. Press, Cambridge, 1991
1991
Earlier work this paper cites.
David Aldous, The continuum random tree III. Ann. Probab. 21
1993
Earlier work this paper cites.
Sara C. Billey, William Jockusch and Richard P. Stanley, Some combinatorial properties of Schubert polynomials. J. Algebraic Combin. 2
1993
Earlier work this paper cites.
Julian West, Generating trees and forbidden subsequences. Discrete Math. 157
1996
Earlier work this paper cites.
Donald E. Knuth, The Art of Computer Programming. Vol. 1: Fundamental Algorithms . 3nd ed., Addison-Wesley, Reading, Mass., 1997
1997
Earlier work this paper cites.
Timothy Chow and Julian West, Forbidden subsequences and Chebyshev polynomials. Discrete Math. 204
1999
Earlier work this paper cites.
Daniel Revuz and Marc Yor, Continuous Martingales and Brownian Motion . 3 r d 3^{rd} edition, Springer-Verlag, Berlin, 1999
1999
Earlier work this paper cites.
Aaron Robertson, Herbert S. Wilf and Doron Zeilberger, Permutation patterns and continued fractions. Electron. J. Combin. 6
1999
Earlier work this paper cites.
Richard P. Stanley, Enumerative Combinatorics , Volume 2, Cambridge Univ. Press, Cambridge, 1999
1999
Earlier work this paper cites.
Toufik Mansour and Alek Vainshtein, Restricted permutations, continued fractions, and Chebyshev polynomials. Electron. J. Combin. 7
2000
Earlier work this paper cites.
Philippe Biane, Jim Pitman and Marc Yor, Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions. Bull. Amer. Math. Soc. (N.S.) 38
2001
Cited alongside, same era.
C. Krattenthaler, Permutations with restricted patterns and Dyck paths. Adv. in Appl. Math. 27
2001
Cited alongside, same era.
Toufik Mansour and Alek Vainshtein, Restricted 132-avoiding permutations. Adv. in Appl. Math. 26
2001
Cited alongside, same era.
T. Mansour and A. Vainshtein, Restricted permutations and Chebyshev polynomials. Sém. Lothar. Combin. 47
2001
Cited alongside, same era.
Olav Kallenberg, Foundations of Modern Probability. 2nd ed., Springer, New York, 2002
2002
Cited alongside, same era.
Michael Drmota, Random Trees . Springer, Vienna, 2009
2009
Later among the works it cites.
James Allen Fill and Svante Janson, Precise logarithmic asymptotics for the right tails of some limit random variables for random trees. Ann. Comb. 12
2009
Later among the works it cites.
Philippe Flajolet and Robert Sedgewick, Analytic Combinatorics . Cambridge Univ. Press, Cambridge, UK, 2009
2009
Later among the works it cites.
Christoph Richard, On q q -functional equations and excursion moments. Discrete Math. 309
2009
Later among the works it cites.
Miklós Bóna, The absence of a pattern and the occurrences of another. Discrete Math. Theor. Comput. Sci. 12
2010
Later among the works it cites.
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2003
Cited alongside, same era.
Jean-François Marckert and Abdelkader Mokkadem, The depth first processes of Galton–Watson trees converge to the same Brownian excursion. Ann. Probab. 31
2003
Cited alongside, same era.
Miklós Bóna, Combinatorics of Permutations . Chapman & Hall/CRC, Boca Raton, FL, 2004
2004
Cited alongside, same era.
Jean-François Marckert, The rotation correspondence is asymptotically a dilatation. Random Structures Algorithms 24
2004
Cited alongside, same era.
Michel Nguyen The, Area and inertial moment of Dyck paths. Combin. Probab. Comput. 13
2004
Cited alongside, same era.
Mireille Bousquet-Mélou and Svante Janson, The density of the ISE and local limit laws for embedded trees. Ann. Appl. Probab. 16
2006
Cited alongside, same era.
2007
Cited alongside, same era.
2010
Later among the works it cites.
M. H. Albert, M. D. Atkinson and Robert Brignall, The enumeration of permutations avoiding 2143 and 4231. Pure Math. Appl. 22
2011
Later among the works it cites.
M. H. Albert, M. D. Atkinson and Robert Brignall, The enumeration of three pattern classes using monotone grid classes. Electron. J. Combin. 19
2012
Later among the works it cites.
Miklós Bóna, Surprising symmetries in objects counted by Catalan numbers. Electron. J. Combin. 19
2012
Later among the works it cites.
Cheyne Homberger, Expected patterns in permutation classes. Electron. J. Combin. 19
2012
Later among the works it cites.
A. Gut, Probability: A Graduate Course . 2nd ed, Springer, New York, 2013
2013
Later among the works it cites.
2013
Later among the works it cites.
Kate Rudolph, Pattern popularity in 132-avoiding permutations. Electron. J. Combin. 20
2013
Later among the works it cites.