0000000000419476

AUTHOR

Cyril Banderier

showing 2 related works from this author

Right-jumps and pattern avoiding permutations

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 sho…

FOS: Computer and information sciencesD-finite function[ MATH.MATH-CV ] Mathematics [math]/Complex Variables [math.CV]Discrete Mathematics (cs.DM)General Computer Scienceinsertion sort[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM][ MATH.MATH-CO ] Mathematics [math]/Combinatorics [math.CO]left-to-right maximumPermutation patternTheoretical Computer Science[ MATH.MATH-NT ] Mathematics [math]/Number Theory [math.NT]Combinatorics[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]FOS: Mathematicsanalytic combinatoricsMathematics - CombinatoricsDiscrete Mathematics and CombinatoricsGolden ratioMathematicsProbability (math.PR)Generating function[ INFO.INFO-DM ] Computer Science [cs]/Discrete Mathematics [cs.DM][MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV]Function (mathematics)[MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT]Exponential function[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]generating functionPermutation patternExponentAnalytic combinatoricssupercongruenceCombinatorics (math.CO)Maxima[ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR]Mathematics - ProbabilityComputer Science - Discrete Mathematics
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Some unusual asymptotics for a variant of insertion sort

2015

International audience

[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO][MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO][ MATH.MATH-CO ] Mathematics [math]/Combinatorics [math.CO]ComputingMilieux_MISCELLANEOUS
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