Publications - I.P. Goulden

• I. P. Goulden and Pavel Shuldiner, Characterizing the number of coloured m-ary partitions modulo m, with and without gaps (PDF) , Discrete Mathematics 341, 2018, 1210-1214.
• I.P. Goulden, Mathieu Guay-Paquet and Jonathan Novak,Toda Equations and Piecewise Polynomiality for Mixed Double Hurwitz Numbers (PDF), SIGMA 12, 2016, 040, 10 pages.
• Valentin Feray, I. P. Goulden, and Alain Lascoux, An edge-weighted hook formula for labelled trees (PDF), Journal of Combinatorics 5, 2014, 245-269.
• I. P. Goulden, M. Guay-Paquet and J. Novak, Monotone Hurwitz Numbers and the HCIZ Integral (PDF), Annales Mathematiques Blaise Pascal 21, 2014, 71-89.
• I. P. Goulden, Mathieu Guay-Paquet and Jonathan Novak, Monotone Hurwitz Numbers in Genus Zero (PDF), Canadian J. Math. 65, 2013, 1020-1042.
• I. P. Goulden, M. Guay-Paquet and J. Novak, Polynomiality of Monotone Hurwitz numbers in Higher Genera (PDF), Advances in Mathematics 238, 2013, 1-23.
• I. P. Goulden and Valentin Feray, A multivariate hook formula for labelled trees (PDF), J. Combinatorial Theory (A) 120, 2013, 944-959.
• Ian P. Goulden, Duc Khiem, Rishikesh and Michael O. Rubinstein, Lower Order Terms for the Moments of Symplectic and Orthogonal Families of L-Functions (PDF), J. Number Theory 133, 2013, 639-674.
• I.P. Goulden, D.M. Jackson and R. Vakil, The moduli space of curves, double Hurwitz numbers, and Faber’s Intersection Number Conjecture (PDF), Annals of Combinatorics 15, 2011, 381-436.
• I.P. Goulden, A. Nica and I. Oancea, Enumerative properties of NC^(B)(p,q) (PDF), Annals of Combinatorics 15, 2011, 277-303.
• S.R. Carrell and I.P. Goulden, Symmetric functions, codes of partitions and the KP hierarchy (PDF), J. Algebraic Combinatorics 32, 2010, 211-226.
• I.P. Goulden and William Slofstra, Annular embeddings of permutations for arbitrary genus (PDF), J. Combinatorial Theory (A) 117, 2010, 272-288.
• I.P. Goulden, D.M. Jackson and R. Vakil, A short proof of the lambda_g-Conjecture without Gromov-Witten theory: Hurwitz theory and the moduli of curves (PDF), J. reine angew. Math. 637, 2009, 175-191.
• I.P. Goulden and D.M. Jackson, Transitive powers of Young-Jucys-Murphy elements are central (PDF), J. Algebra 321, 2009, 1826-1835.
• I.P. Goulden and D.M. Jackson, The KP hierarchy, branched covers, and triangulations (PDF), Advances in Mathematics 219, 2008, 932-951.
• G. Bini, I.P. Goulden and D.M. Jackson, Transitive factorizations in the hyperoctahedral group (PDF), Canadian J. Math. 60, 2008, 297-312.
• I.P. Goulden and A. Rattan, An explicit form for Kerov's character polynomials (PDF), Trans. Amer. Math. Soc. 359, 2007, 3669-3685.
• I.P. Goulden and Luis G. Serrano, A simple recurrence for covers of the sphere with branch points of arbitrary ramification (PDF), Annals of Combinatorics 10, 2006, 431-441.
• John Dollhopf, Ian Goulden and Curtis Greene, Words avoiding a reflexive acyclic relation (PDF), Electronic J. Combinatorics 11(2), 2006, R28
• I.P. Goulden, D.M. Jackson and R. Vakil, Towards the Geometry of Double Hurwitz Numbers (PDF), Advances in Mathematics 198, 2005, 43-92.
• I.P. Goulden, J.H. Kwak, J. Lee, Enumerating branched orientable surface coverings over a non-orientable surface (PDF), Discrete Math 303, 2005, 42-55.
• I.P. Goulden, S. Litsyn and V. Shevelev, On a Sequence Arising in Algebraic Geometry (PDF), Journal of Integer Sequences 8, 2005, Article 05.4.7
• I.P. Goulden and A. Nica, A direct bijection for the Harer-Zagier formula (PDF), J. Combinatorial Theory (A) 111, 2005, 224-238.
• I.P. Goulden, J.H. Kwak, J. Lee, Distributions of regular branched surface coverings (PDF), European J. Combinatorics 25, 2004, 437-455.
• I.P. Goulden and Luis G. Serrano, Maintaining the Spirit of the Reflection Principle when the Boundary has Arbitrary Integer Slope (PDF), J. Combinatorial Theory (A) 104, 2003, 317-326.
• G.E. Andrews, I.P. Goulden and D.M. Jackson, Determinants of random matrices and Jack polynomials of rectangular shape (PDF), Studies Applied Math. 110, 2003, 377-390.
• Ian Goulden and Alexander Yong, Tree-like properties of factorizations (PDF), J. Combinatorial Theory (A) 98, 2002, 106-117.
• Ian Goulden and Alexander Yong, Dyck paths and a bijection for multisets of hook numbers (PDF), Discrete Math. 254, 2002, 153-164.
• I.P. Goulden, D.M. Jackson and R. Vakil, The Gromov-Witten Potential of a Point, Hurwitz Numbers, and Hodge Integrals (PDF), Proc. London Math. Soc. 83, 2001, 563-581.
• I.P. Goulden, J.L. Harer and D.M. Jackson, A geometric parameterization for the virtual Euler characteristic of the moduli spaces of real and complex algebraic curves (PDF), Trans. Amer. Math. Soc. 353, 2001, 4405-4427.
• I.P. Goulden, D.M. Jackson and F.G. Latour, Inequivalent transitive factorizations into transpositions (PDF), Canadian J. Math. 53, 2001, 758-779.
• I.P. Goulden and D.M. Jackson, Transitive factorisations in the symmetric group and combinatorial aspects of singularity theory (PDF), European J. Combinatorics 21, 2000, 1001-1016.
• I.P. Goulden, D.M. Jackson and A. Vainshtein, The number of ramified coverings of the sphere by the torus and surfaces of higher genera (PDF), Annals of Combinatorics 4, 2000, 27-46.
• I.P. Goulden and D.M. Jackson, The number of ramified coverings of the sphere by the double torus, and a general form for higher genera (PDF), J. Combinatorial Theory (A) 88, 1999, 259-275.
• I.P. Goulden and D.M. Jackson, A proof of a conjecture for the number of ramified coverings of the sphere by the torus (PDF), J. Combinatorial Theory (A) 88, 1999, 246-258.
• I.P. Goulden and D.M. Kulkarni, Multivariable Lagrange inversion, Gessel-Viennot cancellation and the Matrix Tree Theorem (PDF), J. Combinatorial Theory (A) 80, 1997, 295-308.
• I.P. Goulden and D.M. Jackson, Maps in locally orientable surfaces, and integrals over real symmetric matrices (PDF), Canadian J. Math. 49, 1997, 865-882.
• I.P. Goulden and D.M. Jackson, Transitive factorisations into transpositions and holomorphic mappings on the sphere (PDF), Proc. Amer. Math. Soc. 125, 1997, 51-60.
• I.P. Goulden and J. West, Raney paths and a combinatorial relationship between nonseparable rooted planar maps and two-stack-sortable permutations (PDF), J. Combinatorial Theory (A) 75, 1996, 220-242.
• I.P. Goulden and D.M. Jackson, Maps in locally orientable surfaces, the double coset algebra, and zonal polynomials (PDF), Canadian J. Math. 48, 1996, 569-584.
• I.P. Goulden, D.M. Jackson and C.M. Springer, An umbral relation between pattern and commutation in strings (PDF), Discrete Math. 158, 1996, 77-85.
• I.P. Goulden and D.M. Jackson, Connection coefficients, matchings, maps and combinatorial conjectures for Jack symmetric functions (PDF), Trans. Amer. Math. Soc. 348, 1996, 873-892.
• I.P. Goulden and D.M. Jackson, Further determinants with the averaging property of Andrews-Burge (PDF), J. Combinatorial Theory (A) 73, 1996, 368-375.
• A.M. Hamel and I.P. Goulden, Planar decompositions of tableaux and Schur function determinants (PDF), European J. Combinatorics 16, 1995, 461-477.
• A.M. Hamel and I.P. Goulden, Lattice paths and a Sergeev-Pragacz formula for skew super symmetric functions (PDF), Canadian J. Math. 47, 1995, 364-382.
• I.P. Goulden and D.M. Jackson, Combinatorial constructions for integrals over normally distributed random matrices (PDF), Proc. Amer. Math. Soc. 123, 1995, 995-1003.
• I.P. Goulden and A.M. Hamel, Shift operators and factorial symmetric functions (PDF), J. Combinatorial Theory (A) 69, 1995, 51-60.
• Ian Goulden and Curtis Greene, A new tableau form for supersymmetric functions (PDF), J. Algebra 170, 1994, 687-703.
• I.P. Goulden, A differential operator for symmetric functions and the combinatorics of multiplying transpositions (PDF), Trans. Amer. Math. Soc. 344, 1994, 421-440.
• I.P. Goulden and D.M. Jackson, Symmetric functions and Macdonald's result for top connexion coefficients in the symmetric group (PDF), J. Algebra 166, 1994, 364-378.
• I.P. Goulden and S. Pepper, Labelled trees and factorizations of a cycle into transpositions (PDF), Discrete Math. 113, 1993, 263-268.
• I.P. Goulden and D.M. Jackson, The combinatorial relationship between trees, cacti, and certain connection coefficients for the symmetric group (PDF), European J. Combinatorics 13, 1992, 357-365.
• I.P. Goulden and D.M. Jackson, Immanants, Schur functions and the MacMahon Master Theorem (PDF), Proc. Amer. Math. Soc. 115, 1992, 605-612.
• I.P. Goulden and D.M. Jackson, Immanants of combinatorial matrices (PDF), J. Algebra 148, 1992, 305-324.
• I.P. Goulden, A linear operator for symmetric functions and tableaux in a strip with given trace (PDF), Discrete Math. 99, 1992, 69-77.
• I.P. Goulden, The number of involutions with r fixed points and a long increasing subsequence, European J. Combinatorics 12, 1991, 109-113.
• I.P. Goulden, Exact values for degree sums over strips of Young diagrams (PDF), Canadian J. Math. 62, 1990, 763-775.
• I.P. Goulden and D.M. Jackson, A combinatorial construction for products of linear transformations over a finite field (PDF), J. Combinatorial Theory (A) 53, 1990, 157-160.
• G.E. Andrews, I.P. Goulden and D.M. Jackson, Generalization of Cauchy's summation theorem for Schur functions (PDF), Trans. Amer. Math. Soc. 310, 1988, 805-820.
• I.P. Goulden, Quadratic forms of skew Schur functions, European J. Combinatorics 9, 1988, 161-168.
• I.P. Goulden, Generating functions and reliabilities for consecutive-k-out-of-n systems, Utilitas Math. 32, 1987, 141-147.
• I.P. Goulden and D.M. Jackson, Labelled graphs with vertices of degree at least three, J. Graph Theory 11, 1987, 177-189.
• D.M. Bressoud and I.P. Goulden, The generalized plasma in one dimension: Evaluation of a partition function (PDF), Communications in Math. Phys. 110, 1987, 287-291.
• G.E. Andrews, I.P. Goulden and D.M. Jackson, Shanks' convergence acceleration transform, Pade approximants and partitions (PDF), J. Combinatorial Theory (A) 43, 1986, 70-84.
• I.P. Goulden and D.M. Jackson, Labelled graphs with small vertex degrees and P-recursiveness (PDF), SIAM Journal on Algebraic and Discrete Methods 7, 1986, 60-66.
• I.P. Goulden and D.M. Jackson, Distributions, continued fractions and the Ehrenfest urn model (PDF), J. Combinatorial Theory (A) 41, 1986, 21-31.
• I.P. Goulden and D.M. Jackson, Path generating functions and continued fractions (PDF), J. Combinatorial Theory (A) 41, 1986, 1-10.
• I.P. Goulden, Directed graphs and the Jacobi-Trudi identity (PDF), Canadian J. Math. 37, 1985, 1201-1210.
• I.P. Goulden, A bijective proof of the q-Saalschutz theorem (PDF), Discrete Math. 57, 1985, 39-44.
• D.M. Bressoud and I.P. Goulden, Constant term identities extending the q-Dyson theorem (PDF), Trans. Amer. Math. Soc. 291, 1985, 203-228.
• I.P. Goulden and D.M. Jackson, Ballot sequences and a determinant of Good's (PDF), J. Combinatorial Theory (A) 40, 1985, 55-61.
• I.P. Goulden, A bijective proof of Stanley's shuffling theorem (PDF), Trans. Amer. Math. Soc. 288, 1985, 147-160.
• I.P. Goulden and D.M. Jackson, A logarithmic connection for circular permutation enumeration, Studies Applied Math. 70, 1984, 121-139.
• I.P. Goulden and D.M. Jackson, An inversion model for q-identities, European J. Combinatorics 4, 1983, 225-230.
• I.P. Goulden, D.M. Jackson and J.W. Reilly, The Hammond series of a symmetric function and its application to P-recursiveness (PDF), SIAM Journal on Algebraic and Discrete Methods 4, 1983, 179-193.
• I.P. Goulden and S.A. Vanstone, The number of solutions to an equation arising from a problem on latin squares, Aust. J. Math. 34, 1983, 138-142.
• I.P. Goulden, A combinatorial proof for a dominance result, Utilitas Math. 22, 1982, 343-347.
• I.P. Goulden and D.M. Jackson, The application of Lagrangian methods to the enumeration of labelled trees with respect to edge partition (PDF), Canadian J. Math. 34, 1982, 513-518.
• I.P. Goulden and D.M. Jackson, Sequence enumeration (PDF), Aeq. Math. 23, 1981, 6-23.
• D.M. Jackson and I.P. Goulden, Algebraic methods for permutations with prescribed patterns (PDF), Advances in Math. 4, 1981, 113-135.
• C.B. Collins, I.P. Goulden, D.M. Jackson and O.M. Nierstrasz, A combinatorial application of matrix Riccati equations and their q-analogue (PDF), Discrete Math. 36, 1981, 139-153.
• I.P. Goulden and D.M. Jackson, The enumeration of directed closed Euler trails and directed Hamiltonian circuits by Lagrangian methods (PDF), European J. Combinatorics 2, 1981, 131-135.
• R.G. Stanton and I.P. Goulden, Graph factorization, general triple systems, and cyclic triple systems (PDF), Aeq. Math. 22, 1981, 1-28.
• D.M. Jackson and I.P. Goulden, The generalisation of Tutte's result for chromatic trees, by Lagrangian methods (PDF), Canadian J. Math. 33, 1981, 12-19.
• I.P. Goulden and D.M. Jackson, A correspondence between plane rooted chromatic trees and generalized derangements (PDF), Bull. Lond. Math. Soc. 13, 1981, 28-32.
• R.G. Stanton, A.N. Arnason and I.P. Goulden, The MacMahon Cube Law, Math. Scientist 6, 1981, 63-72.
• D.M. Jackson and I.P. Goulden, A formal calculus for the enumerative system of sequences: III Further developments, Studies Applied Math. 62, 1980, 131-141.
• D.M. Jackson and I.P. Goulden, A formal calculus for the enumerative system of sequences: II Applications, Studies Applied Math. 61, 1979, 245-277.
• D.M. Jackson and I.P. Goulden, A formal calculus for the enumerative system of sequences: I Combinatorial Theorems, Studies Applied Math. 61, 1979, 141-178.
• I.P. Goulden and D.M. Jackson, The application of algebraic methods to the enumeration of sequences and their q-analogues, Ars Combinatoria 8, 1979, 13-18.
• I.P. Goulden and D.M. Jackson, An inversion theorem for cluster decompositions of sequences with distinguished subsequences (PDF), J. London Math. Soc. (2) 20, 1979, 567-576.
• D.M. Jackson and I.P. Goulden, Sequence enumeration and the de Bruijn-van Aardenne Ehrenfest-Smith-Tutte theorem (PDF), Canadian J. Math. 31, 1979, 488-495.
• R.G. Stanton and I.P. Goulden, Partial sums of some even negative binomials, Ars Combinatoria 5, 1978, 227-236.
• I.P. Goulden, A proof of Fisher's identity, Ars Combinatoria 5, 1978, 7-12.
• I.P. Goulden and D.M. Jackson, The enumeration of generalised alternating subsets with congruences (PDF), Discrete Math. 22, 1978, 99-104.

Papers in refereed conference proceedings

• I.P. Goulden and D.M. Jackson, Connexion coefficients for the symmetric group, free products in operator algebras and random matrices, Fields Institute Proceedings, 12, 1997, 105-125.
• I.P. Goulden and D.M. Jackson, A combinatorial proof of a continued fraction expansion theorem from the Ramanujan notebooks, Proceedings of the Cambridge Combinatorial Conference in Honour of Paul Erdos, 1984, 161-169.
• R.G. Stanton and I.P. Goulden, Some combinatorial polynomials arising from numerical analysis, Proceedings of the 7th Manitoba Conference on Numerical Mathematics and Computing, 1977, 149-160.

• R.G. Dunkley, R.J. MacKay, K.S. Brown, R.F. de Peiza, D.A. DiFelice, I.P. Goulden and D.E. Matthews, Finite Mathematics, Holt, Rinehart and Winston, Toronto, 1988 (502 pages).
• I.P. Goulden and D.M. Jackson, Combinatorial Enumeration, J. Wiley, New York, 1983 (569 pages) (Authorized Russian translation, 1990) (Dover Reprint, 2004).