Computer algebra in the service of enumerative combinatorics
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Publication:6666511
DOI10.1145/3452143.3465507WikidataQ131127664 ScholiaQ131127664MaRDI QIDQ6666511
Publication date: 20 January 2025
generating functionscomputer algebralattice pathsalgebraic functionsenumerative combinatoricsexperimental mathematicscreative telescoping\(d\)-finite functionsguess-and-prove
Cites Work
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- Non-D-finite excursions in the quarter plane
- A fast approach to creative telescoping
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- 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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