Moments of permutation statistics and central limit theorems

DOI10.1016/j.aam.2023.102650arXiv2109.09183MaRDI QIDQ6153611

Niraj Khare, Stoyan Ivanov Dimitrov

Publication date: 14 February 2024

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2109.09183

zbMATH Keywords

permutationscentral limit theoremdescentsstatisticspatternshigher moments

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Exact enumeration problems, generating functions (05A15) Permutations, words, matrices (05A05) Asymptotic enumeration (05A16)

Cites Work

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• Closed expressions for averages of set partition statistics
• Asymptotic behavior of some statistics in Ewens random permutations
• Central limit theorems for some set partition statistics
• Moments of matching statistics
• Patterns in permutations and words.
• The generating function for total displacement
• (2+2)-free posets, ascent sequences and pattern avoiding permutations
• Packing sets of patterns
• Two moments suffice for Poisson approximations: The Chen-Stein method
• Consecutive patterns in permutations
• Generalized permutation patterns and a classification of the Mahonian statistics
• Symbolic moment calculus. I: Foundations and permutation pattern statistics
• A formula for enumerating permutations with a fixed pinnacle set
• On Stanley-Wilf limit of the pattern 1324
• Central limit theorems for patterns in multiset permutations and set partitions
• A structural characterisation of \(\mathrm{Av}(1324)\) and new bounds on its growth rate
• Patterns in trees
• An asymptotic distribution theory for Eulerian recurrences with applications
• Patterns in random permutations
• Combinatorics of Permutations
• Some Probabilistic Aspects of Set Partitions
• Berry-Esseen bounds for combinatorial central limit theorems and pattern occurrences, using zero and size biasing
• The Automatic Central Limit Theorems Generator (and Much More!)
• Gaussian Hilbert Spaces
• A Central Limit Theorem for Vincular Permutation Patterns
• The probability of avoiding consecutive patterns in the Mallows distribution
• Handbook of Enumerative Combinatorics
• Patterns in random permutations avoiding the pattern 321
• Eulerian Numbers
• Patterns in Random Permutations Avoiding the Pattern 132
• The Asymptotic Distribution of Runs of Consecutive Elements
• On a Test for Randomness Based on Signs of Differences
• Note on Runs of Consecutive Elements
• Asymptotic normality of consecutive patterns in permutations encoded by generating trees with one‐dimensional labels

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