Ian Goulden | Academic Influence

Ian Goulden's AcademicInfluence.com Rankings

Ian Goulden

Mathematics

#4463

World Rank

#6334

Historical Rank

Measure Theory

#3612

World Rank

#4263

Historical Rank

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Mathematics

Ian Goulden's Degrees

PhD Mathematics University of Manchester
Bachelors Mathematics University of Manchester

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Why Is Ian Goulden Influential?

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According to Wikipedia, Ian P. Goulden is a Canadian and British mathematician. He works as a professor at the University of Waterloo in the department of Combinatorics and Optimization. He obtained his PhD from the University of Waterloo in 1979 under the supervision of David M. Jackson. His PhD thesis was titled Combinatorial Decompositions in the Theory of Algebraic Enumeration. Goulden is well known for his contributions in enumerative combinatorics such as the Goulden-Jackson cluster method.

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Ian Goulden's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Combinatorial Enumeration (2004) (732)
Transitive factorisations into transpositions and holomorphic mappings on the sphere (1997) (263)
Towards the geometry of double Hurwitz numbers (2003) (140)
The Number of Ramified Coverings of the Sphere by the Torus and Surfaces of Higher Genera (1999) (128)
The combinatorial relationship between trees, cacti and certain connection coefficients for the symmetric group (1992) (128)
The KP hierarchy, branched covers, and triangulations (2008) (113)
AN INVERSION THEOREM FOR CLUSTER DECOMPOSITIONS OF SEQUENCES WITH DISTINGUISHED SUBSEQUENCES (1979) (104)
The Gromov–Witten Potential of A Point, Hurwitz Numbers, and Hodge Integrals (1999) (99)
Monotone Hurwitz Numbers and the HCIZ Integral (2011) (96)
Connection coefficients, matchings, maps and combinatorial conjectures for Jack symmetric functions (1996) (68)
A direct bijection for the Harer-Zagier formula (2005) (66)
A differential operator for symmetric functions and the combinatorics of multiplying transpositions (1994) (62)
Tree-like Properties of Cycle Factorizations (2001) (56)
Raney Paths and a Combinatorial Relationship between Rooted Nonseparable Planar Maps and Two-Stack-Sortable Permutations (1996) (55)
The Number of Ramified Coverings of the Sphere by the Double Torus, and a General Form for Higher Genera (1999) (54)
A Proof of a Conjecture for the Number of Ramified Coverings of the Sphere by the Torus (1999) (51)
A geometric parametrization for the virtual Euler characteristics of the moduli spaces of real and complex algebraic curves (1999) (51)
Maps in Locally Orientable Surfaces, the Double Coset Algebra, and Zonal Polynomials (1996) (46)
Monotone Hurwitz Numbers in Genus Zero (2012) (46)
Planar decompositions of tableaux and Schur function determinants (1995) (45)
Immanants of combinatorial matrices (1992) (42)
Polynomiality of monotone Hurwitz numbers in higher genera (2012) (41)
Maintaining the spirit of the reflection principle when the boundary has arbitrary integer slope (2003) (37)
A short proof of the λg -conjecture without Gromov-Witten theory: Hurwitz theory and the moduli of curves (2009) (37)
Graph factorization, general triple systems, and cyclic triple systems (1981) (36)
The Moduli Space of Curves, Double Hurwitz Numbers, and Faber’s Intersection Number Conjecture (2006) (35)
Maps in Locally Orientable Surfaces and Integrals Over Real Symmetric Surfaces (1997) (35)
Labelled trees and factorizations of a cycle into transpositions (1993) (34)
An explicit form for Kerov's character polynomials (2005) (33)
Constant term identities extending the $q$-Dyson theorem (1985) (31)
Toda Equations and Piecewise Polynomiality for Mixed Double Hurwitz Numbers (2013) (29)
Symmetrical Functions and Macdonald′s Result for Top Connexion Coefficients in the Symmetrical Group (1994) (28)
Monotone Hurwitz numbers and the HCIZ integral II (2011) (26)
The Enumeration of Directed Closed Euler Trails and Directed Hamiltonian Circuits by Lagrangian Methods (1981) (24)
Transitive powers of Young-Jucys-Murphy elements are central (2007) (22)
Shift Operators and Factorial Symmetric Functions (1995) (22)
Transitive Factorizations in the Symmetric Group, and Combinatorial Aspects of Singularity Theory (1999) (21)
A bijective proof of the q-Saalschütz theorem (1985) (18)
A bijective proof of Stanley’s shuffling theorem (1985) (18)
Immanants, Schur functions, and the MacMahon master theorem (1992) (18)
THE HAMMOND SERIES OF A SYMMETRIC FUNCTION AND ITS APPLICATION TO P-RECURSIVENESS* (1983) (17)
A linear operator for symmetric functions and tableaux in a strip with given trace (1992) (16)
Generalizations of Cauchy’s summation theorem for Schur functions (1988) (14)
A Formal Calculus for the Enumerative System of Sequences—I. Combinatorial Theorems (1979) (14)
On the Convergence of Monotone Hurwitz Generating Functions (2016) (12)
Symmetric functions, codes of partitions and the KP hierarchy (2009) (12)
Shanks' convergence acceleration transform, Padé approximants and partitions (1986) (12)
Algebraic Methods for Permutations with Prescribed Patterns (1981) (11)
Annular embeddings of permutations for arbitrary genus (2008) (11)
Words Avoiding a Reflexive Acyclic Relation (2006) (11)
Multivariable Lagrange Inversion, Gessel-Viennot Cancellation, and the Matrix Tree Theorem (1997) (11)
The Generalisation of Tutte's Result for Chromatic Trees, by Lagrangian Methods (1981) (10)
Inequivalent Transitive Factorizations into Transpositions (2001) (10)
Combinatorial constructions for integrals over normally distributed random matrices (1995) (10)
An Inversion Model for q-Identities (1983) (9)
A multivariate hook formula for labelled trees (2012) (9)
Quadratic Forms of Skew Schur Functions (1988) (9)
Determinants of Random Matrices and Jack Polynomials of Rectangular Shape (2003) (8)
Path generating functions and continued fractions (1986) (8)
Distributions, continued fractions, and the Ehrenfest Urn model (1986) (8)
On a Sequence Arising in Algebraic Geometry (2005) (8)
Enumerative Properties of NC(B)(p,q) (2007) (7)
Distributions of regular branched surface coverings (2004) (7)
The generalized plasma in one dimension: Evaluation of a partition function (1987) (7)
Transitive factorizations of permutations and geometry (2014) (7)
A combinatorial application of matrix Riccati equations and their q-analogue (1981) (7)
A Simple Recurrence for Covers of the Sphere With Branch Points of Arbitrary Ramification (2005) (6)
Natural exact covering systems and the reversion of the Möbius series (2017) (6)
A Formal Calculus for the Enumerative System of Sequences—III. Further Developments (1980) (6)
Exact Values for Degree Sums Over Strips of Young Diagrams (1990) (6)
Asymptotics for a Class of Meandric Systems, via the Hasse Diagram of NC(n) (2017) (6)
The enumeration of generalised alternating subsets with congruences (1978) (6)
Further Determinants with the Averaging Property of Andrews-Burge (1996) (5)
Labelled graphs with small vertex degrees and P-recursiveness (1986) (5)
A short proof of the lambda_g-conjecture without Gromov-Witten theory: Hurwitz theory and the moduli of curves (2006) (5)
Lower order terms for the moments of symplectic and orthogonal families of L-functions☆ (2012) (5)
Contents of partitions and the combinatorics of permutation factorizations in genus 0 (2016) (5)
Directed Graphs and the Jacobi-Trudi Identity (1985) (4)
The Application of Lagrangian Methods to the Enumeration of Labelled Trees with Respect to Edge Partition (1982) (4)
Enumerating branched orientable surface coverings over a non-orientable surface (2005) (4)
Dyck paths and a bijection for multisets of hook numbers (2001) (4)
Lattice Paths and a Sergeev-Pragacz Formula for Skew Supersymmetric Functions (1995) (3)
Labelled graphs with vertices of degree at least three (1987) (3)
Sequence Enumeration and the de Bruijn-Van Aardenne Ehrenfest-Smith-Tutte Theorem (1979) (3)
A Correspondence between Plane Planted Chromatic Trees and Generalised Derangements (1981) (3)
Ballot Sequences and a Determinant of Good's (1985) (2)
An edge-weighted hook formula for labelled trees (2013) (2)
The Number of Involutions with r Fixed Points and a Long Increasing Subsequence (1991) (1)
An umbral relation between pattern and commutation in strings (1996) (1)
The number of solutions to an equation arising from a problem on latin squares (1983) (1)
A combinatorial construction for products of linear transformations over a finite field (1990) (0)
A FAMILY OF COMBINATORIAL SOLUTIONS TO THE KP HIERARCHY (2007) (0)
Disjoint covering systems and the reversion of the Möbius series (2017) (0)
CORR 2000-07 Inequivalent Transitive Factorizations into Transpositions (2000) (0)
CORR 99-02 A proof of a conjecture for the number of rami ed coverings of the sphere by the torus* (1999) (0)
Elementary Problems: E2731-E2736 (1978) (0)
On the Convergence of Monotone Hurwitz Generating Functions (2017) (0)
Traumatic Brain Injury (2011) (0)
Sequence enumeration (1981) (0)
Characterizing the number of coloured m-ary partitions modulo m, with and without gaps (2017) (0)
Advanced Problems: 6386-6391 (1982) (0)
J un 2 00 1 Tree-like properties of cycle factorizations (2006) (0)
A logarithmic connection for circular permutation enumeration (1984) (0)
lmmanants of Combinatorial Matrices (2003) (0)
Management of inmate mental health (2009) (0)
A G ] 2 7 Se p 20 03 TOWARDS THE GEOMETRY OF DOUBLE HURWITZ NUMBERS (0)

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