Computer algebra in the service of enumerative combinatorics

DOI10.1145/3452143.3465507WikidataQ131127664 ScholiaQ131127664MaRDI QIDQ6666511

Publication date: 20 January 2025

generating functions computer algebra lattice paths algebraic functions enumerative combinatorics experimental mathematics creative telescoping \(d\)-finite functions guess-and-prove

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30)

Cites Work

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Non-D-finite excursions in the quarter plane
A fast approach to creative telescoping
Walks in the quarter plane: Kreweras' algebraic model
Hypergeometric expressions for generating functions of walks with small steps in the quarter plane
Square lattice walks avoiding a quadrant
The ballot problem with three candidates
An algorithmic proof theory for hypergeometric (ordinary and ``\(q\)) multisum/integral identities
Two non-holonomic lattice walks in the quarter plane
D-finite power series
Classifying lattice walks restricted to the quarter plane
\(G\)-functions and multisum versus holonomic sequences
A probabilistic method for lattice path enumeration
On expansion of algebraic functions in power and Puiseux series. I
Monodromy for the hypergeometric function \(_ nF_{n-1}\)
Differentiably finite power series
Solution of an enumerative problem connected with lattice paths
Factoring polynomials with rational coefficients
The method of creative telescoping
Factorization of differential operators with rational functions coefficients
On those cases in which the Gaussian hypergeometric series represents an algebraic function of its four elements.
Linear recurrences with constant coefficients: The multivariate case
Basic analytic combinatorics of directed lattice paths
Walks confined in a quadrant are not always D-finite
On the functions counting walks with small steps in the quarter plane
An extension of Zeilberger's fast algorithm to general holonomic functions
Winding of simple walks on the square lattice
Linear differential equations as a data structure
Random walks in cones
Bijective counting of Kreweras walks and loopless triangulations
Some open problems related to creative telescoping
Fast computation of special resultants
Polynomial equations with one catalytic variable, algebraic series and map enumeration
Computing hypergeometric solutions of second order linear differential equations using quotients of formal solutions and integral bases
A human proof of Gessel’s lattice path conjecture
Analytic Combinatorics in Several Variables
Modern Computer Algebra
Lattice Path Enumeration
Creative telescoping for rational functions using the griffiths
Second order differential equations with hypergeometric solutions of degree three
Random Walks in the Quarter Plane
Walks with small steps in the quarter plane
Proof of Ira Gessel's lattice path conjecture
Calculating cyclotomic polynomials
Two Parallel Queues Created by Arrivals with Two Demands I
Lost (and Found) in Translation: André's Actual Method and Its Application to the Generalized Ballot Problem
The quasi-holonomic ansatz and restricted lattice walks
General Néron desingularization and approximation
Analysis of PSLQ, an integer relation finding algorithm
A Uniform Approach for the Fast Computation of Matrix-Type Padé Approximants
Counting Walks in the Quarter Plane
The complete generating function for Gessel walks is algebraic
Counting quadrant walks via Tutte's invariant method
Asymptotics of lattice walks via analytic combinatorics in several variables
Generalized Hermite Reduction, Creative Telescoping and Definite Integration of D-Finite Functions
Creative Telescoping for Holonomic Functions
Convergence acceleration during the 20th century

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