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We initiate the study of limit shapes for random permutations avoiding a given pattern.
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E. Deutsch, A. Hildebrand and H. Wilf, Longest increasing subsequences in pattern-restricted permutations, Electron. J. Combin. 9
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T. Mansour and A. Vainshtein, Counting occurences of 132 in a permutation, Adv. Appl. Math 28
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2009
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A. Spiridonov, Pattern-avoidance in binary fillings of grid shapes , Ph.D. Thesis, MIT, 2009, 88 pp
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N. Bernasconi, K. Panagiotou and A. Steger, On properties of random dissections and triangulations, Combinatorica 30
2010
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N. Madras and H. Liu, Random Pattern-Avoiding Permutations, in Algorithmic Probability and Combinatorics , AMS, Providence, RI, 2010, 173–194
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S. Elizalde, Fixed points and excedances in restricted permutations, Electron. J. Combin. 18
2011
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J. Ortmann, Large deviations for non-crossing partitions, Electron. J. Probab. 17
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M. Atapour and N. Madras, Large Deviations and Ratio Limit Theorems for Pattern-Avoiding Permutations, unpublished preprint (2013)
2013
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