An asymptotic distribution theory for Eulerian recurrences with applications

DOI10.1016/j.aam.2019.101960zbMath1440.05026arXiv1807.01412OpenAlexW2981700127WikidataQ126984465 ScholiaQ126984465MaRDI QIDQ2280063

Hua-Huai Chern, Guan-Huei Duh, Hsien-Kuei Hwang

Publication date: 17 December 2019

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

Full work available at URL: https://arxiv.org/abs/1807.01412

zbMATH Keywords

Mittag-Leffler functiongenerating functionsasymptotic normalityrecurrence relationspartial differential equationslimit theoremspermutation statisticsmethod of momentsEulerian numberssingularity analysisBerry-Esseen boundbeta distributionEulerian polynomialsderivative polynomialsquasi-powers approximation

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Exact enumeration problems, generating functions (05A15) Factorials, binomial coefficients, combinatorial functions (05A10) Permutations, words, matrices (05A05) Special sequences and polynomials (11B83) Polynomials and rational functions of one complex variable (30C10) Asymptotic representations in the complex plane (30E15) Combinatorial aspects of groups and algebras (05E16)

Related Items (16)

Random recursive hypergraphs ⋮ Bell numbers in Matsunaga's and Arima's Genjikō combinatorics: modern perspectives and local limit theorems ⋮ A half-normal distribution scheme for generating functions ⋮ Stirling permutation codes ⋮ Positivity of Narayana polynomials and Eulerian polynomials ⋮ Moments of permutation statistics and central limit theorems ⋮ Exactly solvable urn models under random replacement schemes and their applications ⋮ Excedance-type polynomials, gamma-positivity and alternatingly increasing property ⋮ Eulerian polynomials and the 𝑔-indices of Young tableaux ⋮ Analytic combinatorics of coordination numbers of cubic lattices ⋮ Asymptotic normality in t-stack sortable permutations ⋮ Analytic properties of combinatorial triangles related to Motzkin numbers ⋮ On the joint distribution of descents and signs of permutations ⋮ Asymptotic normality of the number of corners in tableaux associated with the partially asymmetric simple exclusion process ⋮ Eulerian pairs and Eulerian recurrence systems ⋮ Random decompositions of Eulerian statistics

Uses Software

• OEIS

Cites Work

• New Eulerian numbers of type \(D\)
• Some identities of the \(r\)-Whitney numbers
• Counting permutations by runs
• Occupied corners in tree-like tableaux
• General Eulerian numbers and Eulerian polynomials
• Enumeration of permutations by number of alternating runs
• A generalization of carries processes and Eulerian numbers
• Tree-like tableaux
• The tree structure in staircase tableaux
• The \({1/k}\)-Eulerian polynomials
• An explicit formula for the number of permutations with a given number of alternating runs
• Generalized Stirling permutations, families of increasing trees and urn models
• A history of the central limit theorem. From classical to modern probability theory
• Polynomial solutions of differential-difference equations
• Asymptotic properties of \(B\)-splines, Eulerian numbers and cube slicing
• Derivative polynomials and enumeration of permutations by number of interior and left peaks
• General combinatorial schemas: Gaussian limit distributions and exponential tails
• On a generalization of Morisita's model for estimating the habitat preference
• On the anti-exceedance distribution on the symmetric group and its subgroups
• Legendre-Stirling permutations
• Some polynomials associated with the \(r\)-Whitney numbers
• Eulerian numbers and polynomials of higher order
• Generalized Stirling permutations and forests: higher-order Eulerian and Ward numbers
• Faces of generalized permutohedra
• Thomas Harriot's doctrine of triangular numbers: The ``Magisteria Magna
• Variations on descents and inversions in permutations
• Carries, shuffling, and symmetric functions
• Statistical tests on two characteristics of the shapes of cluster diagrams
• Recurrences and formulae in an extension of the Eulerian numbers
• Eulerian numbers, Newcomb's problem and representations of symmetric groups
• Central and local limit theorems applied to asymptotic enumeration. IV: Multivariate generating functions
• Super ballot numbers
• On a generalized Eulerian distribution
• Some properties of the generalized Eulerian distribution
• The number of increases in a random permutation
• Stirling polynomials
• On convergence rates in the central limit theorems for combinatorial structures
• On certain summation problems and generalizations of Eulerian polynomials and numbers
• Constraint-sensitive Catalan path statistics having the Narayana distribution
• Permutation statistics of indexed permutations
• A generalization of the Eulerian numbers with a probabilistic application
• Some permutation representations of Weyl groups associated with the cohomology of toric varieties
• \(q\)-Eulerian polynomials arising from Coxeter groups
• The rook numbers of Ferrers boards and the related restricted permutation numbers
• Probabilistic bounds on the coefficients of polynomials with only real zeros
• Some geometric probability problems involving the Eulerian numbers
• Enumeration of permutations and sequences with restrictions
• Second phase changes in random \(m\)-ary search trees and generalized quicksort: Convergence rates
• Consecutive patterns in permutations
• Some applications of the generalized Eulerian numbers
• The necklace process: a generating function approach
• A central limit theorem for a new statistic on permutations
• Eulerian numbers associated with arithmetical progressions
• On the Lambert \(w\) function
• A probabilistic interpretation of Eulerian numbers
• Legendre polynomials, Legendre--Stirling numbers, and the left-definite spectral analysis of the Legendre differential expression
• On the Eulerian polynomials of type \(D\).
• On the roots of orthogonal polynomials and Euler-Frobenius polynomials
• A family of two-variable derivative polynomials for tangent and secant
• Some remarks on the joint distribution of descents and inverse descents
• Diagonal checker-jumping and Eulerian numbers for color-signed permutations
• Gamma-positivity of variations of Eulerian polynomials
• Derangement polynomials and excedances of type \(B\)
• A unified approach to polynomial sequences with only real zeros
• Eulerian polynomials, Stirling permutations of the second kind and perfect matchings
• Distribution of descents in matchings
• Counting signed permutations by their alternating runs
• A refined sign-balance of simsun permutations
• Bivariate generating functions for a class of linear recurrences: general structure
• Exact moments and probabilities for Wei's urn randomization model
• Some combinatorial arrays generated by context-free grammars
• Strong \(q\)-log-convexity of the Eulerian polynomials of Coxeter groups
• On Polya frequency functions. IV: The fundamental spline functions and their limits
• Eulerian numbers of higher order
• Enumeration of permutations of \((1, \ldots, n)\) by number of maxima
• Théorie géométrique des polynômes eulériens
• Central and local limit theorems applied to asymptotic enumeration
• Functional limit theorems for multitype branching processes and generalized Pólya urns.
• Relationship between Morisita's model for estimating the environmental density and the generalized Eulerian numbers
• Normal approximations for descents and inversions of permutations of multisets
• Eine neue Einteilung der Permutationen
• The central limit theorem for dependent random variables
• Congruences for Eulerian numbers
• The problem of the rooks and its applications
• The Generalized Pascal Triangle and the Matrix Variate Jensen-Logistic Distribution
• Combinatorics: Ancient and Modern
• Euler–Frobenius numbers
• Two-Sided Eulerian Numbers via Balls in Boxes
• ON -VECTORS AND THE DERIVATIVES OF THE TANGENT AND SECANT FUNCTIONS
• Unimodality, log-concavity, real-rootedness and beyond
• Plane recursive trees, Stirling permutations and an urn model
• Exponential bounds for normal approximation of the number of descents and inversions
• ENUMERATION OF A DUAL SET OF STIRLING PERMUTATIONS BY THEIR ALTERNATING RUNS
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• Descent numbers and major indices for the hyperoctahedral group
• Generalisations of the Euler adic
• Two Notes on Notation
• A Generalisation of Stirling's Formula.
• Eulerian Numbers and Polynomials
• Unimodal, log-concave and Pólya frequency sequences in combinatorics
• Unimodal Polynomials Arising from Symmetric Functions
• Singularity Analysis of Generating Functions
• Efficient Serial Message-Passing Schedules for LDPC Decoding
• Asymptotic Normality in the Generalized Polya–Eggenberger Urn Model, with an Application to Computer Data Structures
• Interesting Series Involving the Central Binomial Coefficient
• Permutations and sequences with repetitions by number of increases
• The Frobenius–Harper technique in a general recurrence model
• Eulerian number asymptotics
• Images and Preimages in Random Mappings
• Low–dimensional lattices. VII. Coordination sequences
• Characterization of B-Spline Digital Filters
• Probabilistic consequences of some polynomial recurrences
• Corners in tree-like tableaux
• Asymptotic Normality of Scaling Functions
• On the structure of random plane‐oriented recursive trees and their branches
• An asymptotic theory for Cauchy–Euler differential equations with applications to the analysis of algorithms
• Peaks and Eulerian numbers in a random sequence
• Greek letters in random staircase tableaux
• Real Zeros and Normal Distribution for Statistics on Stirling Permutations Defined by Gessel and Stanley
• Limit distribution of the coefficients of polynomials with only unit roots
• Eulerian Numbers
• Some Aspects of the Random Sequence
• The Necklace Process
• Estimating the Error of a Permutational Central Limit Theorem
• Euler-Frobenius numbers and rounding
• Mittag-Leffler Functions, Related Topics and Applications
• Bernard Friedman's Urn
• The Coefficients in an Asymptotic Expansion
• Stirling Behavior is Asymptotically Normal
• Asymptotic properties of eulerian numbers
• Enumeration of permutations by rises and cycle structure.
• Exponential integral integral infinity 1 e-xtt -ndt for large values of n
• On a memory game and preferential attachment graphs
• Some Properties of Points Arranged at Random on a Möbius Surface
• THE GENERALIZED BESSEL FUNCTION OF ORDER GREATER THAN ONE
• On Fluctuations in Coin-Tossing
• The fundamental limit theorems in probability
• On a Test for Randomness Based on Signs of Differences
• Time Series Significance Tests Based on Signs of Differences
• Asymptotic Distribution of Runs Up and Down
• On the string-theoretic Euler number of a class of absolutely isolated singularities

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