PUBLICATIONS:

Papers in refereed journals:

• I. P. Goulden, Mathieu Guay-Paquet and Jonathan Novak, Monotone Hurwitz Numbers in Genus Zero, Canadian J. Math., accepted August, 2012. (pdf file)

• Ian P. Goulden, Duc Khiem, Rishikesh and Michael O. Rubinstein, Lower Order Terms for the Moments of Symplectic and Orthogonal Families of L-Functions, J. Number Theory 133, 2013, 639-674. (pdf file)

• I.P. Goulden, D.M. Jackson and R. Vakil, The moduli space of curves, double Hurwitz numbers, Annals of Combinatorics 15, 2011, 381-436. (pdf file)

• I.P. Goulden, A. Nica and I. Oancea, Enumerative properties of NC^(B)(p,q), Annals of Combinatorics 15, 2011, 277-303. (pdf file)

• S.R. Carrell and I.P. Goulden, Symmetric functions, codes of partitions and the KP hierarchy, J. Algebraic Combinatorics 32, 2010, 211-22 6. (pdf file)

• I.P. Goulden and William Slofstra, Annular embeddings of permutations for arbitrary genus, J. Combinatorial Theory (A) 117, 2010, 272-288. (pdf file)

• 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, J. reine angew. Math. 637, 2009, 175-191. (pdf file)

• I.P. Goulden and D.M. Jackson, Transitive powers of Young-Jucys-Murphy elements are central, J. Algebra 321, 2009, 1826-1835. (pdf file)

• I.P. Goulden and D.M. Jackson, The KP hierarchy, branched covers, and triangulations, Advances in Mathematics 219, 2008, 932-951. (pdf file)

• G. Bini, I.P. Goulden and D.M. Jackson, Transitive factorizations in the hyperoctahedral group, Canadian J. Math. 60, 2008, 297-312. (pdf file)

• I.P. Goulden and A. Rattan, An explicit form for Kerov's character polynomials, Trans. Amer. Math. Soc. 359, 2007, 3669-3685. (Published form)

• I.P. Goulden and Luis G. Serrano, A simple recurrence for covers of the sphere with branch points of arbitrary ramification, Annals of Combinatorics 10, 2006, 431-441. (pdf file)

• John Dollhopf, Ian Goulden and Curtis Greene, Words avoiding a reflexive acyclic relation, Electronic J. Combinatorics 11(2), 2006, R28 (Published form)

• I.P. Goulden, D.M. Jackson and R. Vakil, Towards the Geometry of Double Hurwitz Numbers, Advances in Mathematics 198, 2005, 43-92. (pdf file)

• I.P. Goulden, J.H. Kwak, J. Lee, Enumerating branched orientable surface coverings over a non-orientable surface, Discrete Math 303, 2005, 42-55.

• I.P. Goulden, S. Litsyn and V. Shevelev, On a Sequence Arising in Algebraic Geometry, Journal of Integer Sequences 8, 2005, Article 05.4.7 (Published form)

• I.P. Goulden and A. Nica, A direct bijection for the Harer-Zagier formula, J. Combinatorial Theory (A) 111, 2005, 224-238. (pdf file)

• I.P. Goulden, J.H. Kwak, J. Lee, Distributions of regular branched surface coverings, 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, J. Combinatorial Theory (A) 104, 2003, 317-326. (pdf file)

• G.E. Andrews, I.P. Goulden and D.M. Jackson, Determinants of random matrices and Jack polynomials of rectangular shape, Studies Applied Math. 110, 2003, 377-390. (pdf file)

• Ian Goulden and Alexander Yong, Tree-like properties of factorizations, J. Combinatorial Theory (A) 98, 2002, 106-117.

• Ian Goulden and Alexander Yong, Dyck paths and a bijection for multisets of hook numbers, 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, 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, Trans. Amer. Math. Soc. 353, 2001, 4405-4427.

• I.P. Goulden, D.M. Jackson and F.G. Latour, Inequivalent transitive factorizations into transpositions, 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, 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, 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, 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, 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, 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, Canadian J. Math. 49, 1997, 865-882.

• I.P. Goulden and D.M. Jackson, Transitive factorisations into transpositions and holomorphic mappings on the sphere, 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, J. Combinatorial Theory (A) 75, 1996, 220-242.

• I.P. Goulden and D.M. Jackson, Maps in locally orientable surfaces, the doubl e coset algebra, and zonal polynomials, Canadian J. Math. 48, 1996, 569-584.

• I.P. Goulden, D.M. Jackson and C.M. Springer, An umbral relation between patt ern and commutation in strings, Discrete Math. 158, 1996, 77-85.

• I.P. Goulden and D.M. Jackson, Connection coefficients, matchings, maps and combinatorial conjectures for Jack symmetric functions, Trans. Amer. Math. Soc. 348, 1996, 873-892.

• I.P. Goulden and D.M. Jackson, Further determinants with the averaging property of Andrews-Burge, J. Combinatorial Theory (A) 73, 1996, 368-375.

• A.M. Hamel and I.P. Goulden, Planar decompositions of tableaux and Schur function determinants, 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, Canadian J. Math. 47, 1995, 364-382.

• I.P. Goulden and D.M. Jackson, Combinatorial constructions for integrals over normally distributed random matrices, Proc. Amer. Math. Soc. 123, 1995, 995-1003.

• I.P. Goulden and A.M. Hamel, Shift operators and factorial symmetric functions, J. Combinatorial Theory (A) 69, 1995, 51-60.

• Ian Goulden and Curtis Greene, A new tableau form for supersymmetric functions, J. Algebra 170, 1994, 687-703.

• I.P. Goulden, A differential operator for symmetric functions and the combinatorics of multiplying transpositions, 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, J. Algebra 166, 1994, 364-378.

• I.P. Goulden and S. Pepper, Labelled trees and factorizations of a cycle into transpositions, 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, European J. Combinatorics 13, 1992, 357-365.

• I.P. Goulden and D.M. Jackson, Immanants, Schur functions and the MacMahon Master Theorem, Proc. Amer. Math. Soc. 115, 1992, 605-612.

• I.P. Goulden and D.M. Jackson, Immanants of combinatorial matrices, J. Algebra 148, 1992, 305-324.

• I.P. Goulden, A linear operator for symmetric functions and tableaux in a strip with given trace, 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, 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, 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, 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, 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, J. Combinatorial Theory (A) 43, 1986, 70-84.

• I.P. Goulden and D.M. Jackson, Labelled graphs with small vertex degrees and P-recursiveness, 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, J. Combinatorial Theory (A) 41, 1986, 21-31.

• I.P. Goulden and D.M. Jackson, Path generating functions and continued fractions, J. Combinatorial Theory (A) 41, 1986, 1-10.

• I.P. Goulden, Directed graphs and the Jacobi-Trudi identity, Canad. J. Math. 37, 1985, 1201-1210.

• I.P. Goulden, A bijective proof of the q-Saalschutz theorem, Discrete Math. 57, 1985, 39-44.

• D.M. Bressoud and I.P. Goulden, Constant term identities extending the q-Dyson theorem, Trans. Amer. Math. Soc. 291, 1985, 203-228.

• I.P. Goulden and D.M. Jackson, Ballot sequences and a determinant of Good's, J. Combinatorial Theory (A) 40, 1985, 55-61.

• I.P. Goulden, A bijective proof of Stanley's shuffling theorem, 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, 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, Canad. J. Math. 34, 1982, 513-518.

• I.P. Goulden and D.M. Jackson, Sequence enumeration, Aeq. Math. 23, 1981, 6-23.

• D.M. Jackson and I.P. Goulden, Algebraic methods for permutations with prescribed patterns, 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, 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, European J. Combinatorics 2, 1981, 131-135.

• R.G. Stanton and I.P. Goulden, Graph factorization, general triple systems, and cyclic triple systems, 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, Canad. J. Math. 33, 1981, 12-19.

• I.P. Goulden and D.M. Jackson, A correspondence between plane rooted chromatic trees and generalized derangements, 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, 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, Canad. 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, 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.

Books:

• 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).