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Right-jumps and pattern avoiding permuta...
Banderier, Cyril...

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Right-jumps and pattern avoiding permutations by Banderier, Cyril ( Author )
Lemonjar Open Access
N.A
07-12-2015
We study the iteration of the process "a particle jumps to the right" in permutations. We prove that the set of permutations obtained in this model after a given number of iterations from the identity is a class of pattern avoiding permutations. We characterize the elements of the basis of this class and we enumerate these "forbidden minimal patterns" by giving their bivariate exponential generating function: we achieve this via a catalytic variable, the number of left-to-right maxima. We show that this generating function is a D-finite function satisfying a nice differential equation of order~2. We give some congruence properties for the coefficients of this generating function, and we show that their asymptotics involves a rather unusual algebraic exponent (the golden ratio (1+5–√)/2) and some unusual closed-form constants. We end by proving a limit law: a forbidden pattern of length n has typically (lnn)/5–√ left-to-right maxima, with Gaussian fluctuations.
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Article
pdf
36.88 KB
English
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MYR 0.01
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https://arxiv.org/abs/1512.02171
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