David M. R. Jackson

Notes

1. "Linear algebra with advanced application" (temporary title). (with G.W.Bennett)

2. "An introduction to Quantum and Vassiliev Invariants of Knots". Advanced undergraduate and graduate notes that are also addressed to combinatorialists who are interested in invariants of knots. They are written in a way that shows algebra at work in a context that combines both topology and combinatorial constructions. Emphasis is place on full exposition of the material that is included. Included are Reidemeister's Theorem, Markov's Theorem, the braid group, a representation of the braid group, the Yang-Baxter equation and a solution to it, Turaev's Theorem, Vassiliev invariants, chord diagrams, Jacobi diagrams, the Lie bracket, Jacobi's identity, Penrose's diagrammatic calculus, Kontsevich's universality theorem, the relationship between quantum invariants of knots and Lie algebras, an introduction to invariants of 3-manifolds, the Kirby moves, and the Temperley-Lieb algebra. Also included is the necessary material on Hopf algebras, ribbon Hopf algebras, and Lie algebras. (with I. Moffatt)

III) Books:

1. An Introduction to Quantum and Vassiliev Knot Invariants, (with I. Moffatt). CMS Books in Mathematics, Springer. To appear in June 2019.

   See II(2) above for comments on content.

2. An Atlas of the Smaller Maps on Orientable and Nonorientable Surfaces, Chapman Hall/CRC, New York, 2000, xi + 279 pages, (with T.I.Visentin). This is a collection of drawings of polygonal representations of maps with a small number of edges in orientable and non-orientable surfaces and tables of map numbers, together with an account of the Quadrangulation Conjecture and the b-Conjecture. There is a 70 page Introduction to maps.

3. Combinatorial Enumeration, Wiley, New York, 1983, xxiv + 569 pages, with a Foreword by Gian-Carlo Rota. (with I.P.Goulden). This is a research level book with a large number of exercises, many of which are based on research papers.
   • Russian translation of this book, published by "Nauka," Moscow, 1990.
   • Unabridged republication in a Dover edition in 2004.

IV) Papers:

2018

1. Combinatorial Aspects of the Quantized Universal Enveloping Algebra of sl_(n+1). Annals of Combinatorics, 22 (2018), 681--710. (with R. Chang and G.J. Stanley).

   2016

2. A robust generalization of the Legendre transform. arXiv : 1612.004 v1 [hep:th] 1 Dec 2016 (with A.Kempf and A.H.Morales).
3. Transitive factorizations of permutations and geometry. (with I.P.Goulden). In: The Mathematical Legacy of Richard P.Stanley, Eds. P.Hersh, T.Lam, P.Pylyavskyy, V.Reiner. American Mathematical Society, 2016. (189 -- 201).

   2015

4. How to (Path-) integrate by differentiating. J. Phys.: Conf. Ser. 626, 012015 (2015) (with A.Kempf and A.H.Morales).

   2014

5. New Dirac delta function based methods with applications to perturbative expansions in quantum field theory. J. Phys. A: Math. Theor. 47 (2014) 415204 (12pp). (with A.Kempf and A.H.Morales).

   2012

6. Near-central permutation factorization and Strahov's generalized Murnaghan-Nakayama rule. J. Combinatorial Theory (A), 119 (2012), 1856--1874. (with C.A.Sloss).
7. Character-theoretic techniques for near-central enumerative problems. J. Combinatorial Theory (A), 119 (2012), 1665--1679. (with C.Sloss).

   2011

8. The moduli space of curves, double Hurwitz numbers, and Faber's intersection number conjecture. Ann. Comb., 15 (2011) 381--436. (with I.P.Goulden and R.Vakil).

   2010

9. On Tutte's chromatic invariant, Trans. AMS., 362 (2010) 491--507. (with S.Cautis).

   2009

10. 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. (with I.P.Goulden and R.Vakil).
11. Transitive powers of Young-Jucys-Murphy elements are central. J.Algebra, 321 2009, 1826--1835. (with I.P.Goulden).

    2008

12. Transitive factorizations in the hypoctahedral group, Canad. J. Math., 60 (2008), 297--312. (with G.Bini and I.P.Goulden).
13. The KP hierarchy, branched covers and triangulations, Adv. Math., 219 2008, 932--951. (with I.P.Goulden).
14. On the structure of QFT in the Particle Picture of the Path Integral Formulation. arXiv:0810.4293 [hep-th]. (with A.Kempf and A.Morales).

    2007

15. On the group-like behaviour of the Le-Murakami-Ohtsuki invariant. J. Knot Theory and its Ramifications, 16 (2007) 669--718. (with I. Moffatt and M. Morales).

    2006

16. A symmetric function resolution of the number of permutations with respect to block-stable elements. Annals. Combinatorics, 10 (2006) 463--480. (with M. Yip).
17. A rooted map invariant, non-orientability and Jack symmetric functions, J. Combinatorial Theory (B), 97 (2007) 430--452. (with D.R.L.Brown).

    2005

18. Towards the geometry of the double Hurwitz numbers, Advances in Mathematics, Volume dedicated to the 70th Birthday of Michael Artin, 198 (2005) 43--92 (with I.P.Goulden and R. Vakil).

    2003

19. The matrix of chromatic joins and the Temperley-Lieb algebra, J. Combinatorial Theory (B) 89 (2003) 109--155. (with S.Cautis).
20. Determinants of random matrices and Jack polynomials of rectangular shape. Studies Applied Math. 110 (2003) 377--390. (with G.E.Andrews and I.P.Goulden)

    2002

21. The quadrangulation conjecture for orientable surfaces, J. Combinatorial Theory (B) 86 (2002) 54--79. (with D.R.L.Brown)

    2001

22. The Gromov-Witten potential of a point, Hurwitz numbers, and Hodge integrals. Proc. London Math. Soc. 83 (2001) 563--581. (with I.P.Goulden and R.Vakil)
23. A geometric parametrization for the virtual Euler characteristic of the moduli spaces of real and complex algebraic curves, Trans. AMS 353 (2001) 4005--4427. (with I.P.Goulden and J.L.Harer)
24. Inequivalent transitive factorizations into transpositions. Canad. J. Math. 53 (2001) 758--779 (with I.P.Goulden and F.G.Latour)

    2000

25. Transitive factorisations in the symmetric group, and combinatorial aspects of singularity theory. Europ. J. Combinatorics 21 (2000) 1001--1016. (with I.P.Goulden)
26. The number of ramified coverings of the sphere by the torus and surfaces of higher genera, Annals of Combinatorics 4 (2000) 27--46. (with I.P.Goulden and A.Vainshtein)

    1999

27. A combinatorial relationship between Eulerian maps and hypermaps in orientable surfaces, J. Combinatorial Theory (A) 78 (1999) 120--150. (with T.I.Visentin)
28. 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. (with I.P.Goulden)
29. 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. (with I.P.Goulden)

    1997

30. Transitive factorisations into transpositions and holomorphic mappings on the sphere, Proc. AMS 125 (1997) 51--60. (with I.P.Goulden)
31. Maps in locally orientable surfaces and integrals over real symmetric matrices, Canad. J. Math. 48 (1997) 865--882. (with I.P.Goulden)
32. Connexion coefficients for the symmetric group, free products in operator algebras and random matrices, Fields Institute Communications 12 (1997) 105--125. (with I.P.Goulden)

    1996

33. Factorisations for partition functions of random Hermitian matrix models, Comm. Math. Phys. 179 (1996) 25--60. (with M.J.Perry and T.I.Visentin)
34. Maps in locally orientable surfaces, the double coset algebra, and zonal polynomials, Canad. J. Math. 48 (1996) 569--584. (with I.P.Goulden)
35. Connection coefficients, matchings, maps, and combinatorial conjectures for Jack symmetric functions, Trans. AMS 348 (1996) 873--892. (with I.P.Goulden)
36. A formulation for the genus series for regular maps, J. Combinatorial Theory (A) 74 (1996) 14--32. (with T.I.Visentin)
37. Algebraic and analytic approaches for the genus series for 2-cell embeddings on orientable and nonorientable surfaces, DIMACS Series in Discrete Math. and Theoretical Computer Science, Vol. 24, 1996, 115--132. AMS, Providence, RI.
38. Further determinants with the averaging property of Andrews-Burge, J. Combinatorial Theory (A) 73 (1996) 368--375. (with I.P.Goulden)
39. An umbral relation between pattern and commutation in strings, Discrete Math. 158 (1996) 77-85. (with I.P.Goulden, and C.Springer)
40. Research Problems 246, 247, 248. In: Research Problems, Discrete Math. 157 (1996) 375--388.

    1995

41. Combinatorial constructions for integrals over normally distributed random matrices, Proc. AMS 123 (1995) 995--1003. (with I.P.Goulden)
42. The genus series for maps, J. Pure and Applied Algebra 105 (1995) 293--297.

    1994

43. A hypergeometric analysis of the genus series for a class of 2-cell embeddings in orientable surfaces, SIAM J. Math. Anal. 25 (1994) 243--255. (with G.E.Andrews and T.I.Visentin)
44. On an integral representation for the genus series for 2-cell embeddings, Trans. AMS 344 (1994) 755--772.
45. Symmetric functions and Macdonald's result for top connexion coefficients in the symmetric group, J. Algebra 166 (1994) 364--378. (wth I.P.Goulden)
46. The lattice of non-crossing partitions and the Birkhoff-Lewis equations, Europ. J. Combinatorics 15 (1994) 245--250.

    1992

47. Immanants of combinatorial matrices, J. Algebra 148 (1992) 305--324. (with I.P.Goulden)
48. Immanants, Schur functions and the MacMahon Master theorem, Proc. AMS 115 (1992) 605--612. (with I.P.Goulden)
49. The combinatorial relationship between trees, cacti and certain connection coefficients for the symmetric group, Europ. J. Combinatorics 12 (1992) 357--365. (with I.P.Goulden)
50. The asymptotic behaviour of three-connected triangulations of the disk, with a reflective symmetry in a line, Combinatorica 12 (1992) 149--153. (with L.B.Richmond)
51. A D-finiteness result for products of permutations, Discrete Math. 99 (1992) 25-30. (with E.R.Canfield)

    1990

52. An algebrically derived q-analogue of a character sum associated with a class of semi-regular permutations, Pac. J. Math. 144 (1990) 207--218. (with G.E.Andrews)
53. A character theoretic approach to embeddings of rooted maps in an orientable surface of given genus, Trans. AMS 322 (1990) 343--363. (with T.I.Visentin)
54. A character theoretic approach to embeddings of rooted maps in an orientable surface of given genus: face-coloured maps, Trans. AMS 322 (1990) 365--376. (with T.I.Visentin)
55. A combinatorial construction for products of linear transformations over a finite field, J. Combinatorial Theory (A) 53 (1990) 157--160. (with I.P.Goulden)

    1989

56. Proceedings of the Oberwolfach Meeting "Kombinatorik", Oberwolfach, January 19 - January 25, 1986, Discrete. Math. Special Double Issue, eds. W.Deuber, D.M.Jackson and D.Jungnickel, 73(1-2) (1988/89)

    1988

57. Counting semiregular permutations which are products of a full cycle and an involution, Trans. AMS 305 (1988) 317--331.
58. Some combinatorial problems associated with products of conjugacy classes of the symmetric group, J. Combinatorial Theory (A) 49 (1988) 363--369.
59. Generalisations of Cauchy's summation theorem for Schur functions, Trans. AMS 310 (1988) 805--820. (with G.E.Andrews and I.P.Goulden)
60. Generating function methods for macromolecules at surfaces. II. One molecule between two planes, J. Chem. Phys. 88 (1988) 5171-5180. (with B.E.Eichinger and B.D.McKay)

    1987

61. Counting cycles in permutations by group characters, with an application to a topological problem, Trans. AMS 299 (1987) 785--801.
62. Labelled graphs with vertices of degree at least three, J. Graph Theory 11 (1987) 177--189. (with I.P.Goulden)

    1986

63. Distributions, continued fractions and the Ehrenfest urn model, J. Combinatorial Theory (A) 41 (1986) 21--31. (with I.P.Goulden)
64. Path generating functions and continued fractions, J. Combinatorial Theory (A) 41 (1986) 1--10. (with I.P.Goulden)
65. Generating function methods for macromolecules at surfaces. I. One molecule at a plane surface, J. Chem. Phys. 85 (1986) 5299--5305. (with B.E.Eichinger and B.D.McKay)
66. Shank's convergence acceleration transform, Pade approximants and partitions, J. Combinatorial Theory (A) 43 (1986) 70--84. (with G.E.Andrews and I.P.Goulden)
67. Labelled graphs with small vertex degrees and P-recursiveness, SIAM J. Alg. Discrete Meth. 7 (1986) 6--66. (with I.P.Goulden)

    1985

68. Ballot sequences and a determinants of Good's, J. Combinatorial Theory (A) 40 (1985) 55--61. (with I.P.Goulden)

    1984

69. A logarithmic connexion for circular permutation enumeration, Studies Appl. Math. 70 (1984) 121--139. (with I.P.Goulden)
70. "Enumeration and Design," Proceedings of the Silver Jubilee Conference on Combinatorics, June 14 - July 2, 1982, University of Waterloo, Waterloo, Ontario, Canada; eds. D.M.Jackson and S.A.Vanstone, Academic Press, New York, 1984.

    1983

71. A combinatorial proof of a continued fraction expansion theorem from the Ramanujan Notebooks, In: "Graph Theory and Combinatorics" (Cambridge 1983) Academic Press, New York 1984, 97--116. (with I.P.Goulden)
72. The Hammond series of a symmetric function and its application to P-recursiveness, SIAM J. Alg. Discrete Meth. 4 (1983) 179--193. (with I.P.Goulden and J.W.Reilly)
73. An inversion model for q-identities, Europ. J. Combinatorics 4 (1983) 225--230. (with I.P.Goulden)

    1982

74. The enumeration of covers of a finite set, J. London Math. Soc. 25 (1982) 1--6. (with J.S.Devitt)
75. The application of Lagrangian methods to the enumeration of labelled trees with respect to edge partition, Canad. J. Math. 34 (1982) 513-518. (with I.P.Goulden)

    1981

76. A correspondence between plane planted chromatic trees and generalised derangements, Bull. London Math. Soc. 13 (1981) 28-32. (with I.P.Goulden)
77. The generalisation of Tutte's result for chromatic trees, by Lagrangian methods, Canad. J. Math. 33 (1981) 12--19. (with I.P.Goulden)
78. The enumeration of directed closed Euler trails and directed Hamiltonian circuits by Lagrangian methods, Europ. J. Combinatorics, 2 (1981) 131--135. (with I.P.Goulden)
79. A combinatorial application of matrix Riccati equations and their q-analogue, Discrete Math. 36 (1981) 139--153. (with C.B.Collins, I.P.Goulden and O.M.Nierstracz).
80. Sequence enumeration, Aequationes Math. 23 (1981) 6--23. (with I.P.Goulden)
81. Algebraic metods for permutations with prescribed patterns, Advances in Math. 42 (1981) 113--135. (with I.P.Goulden)
82. Comma-free codes: an extension of certain enumerative techniques to recursively defined sequences, J. Combinatorial Theory (A) 30 (1981) 1--18. (with J.S. Devitt)

    1980

83. A formal calculus for the enumerative system of sequences - III. Further developments, Studies Appl. Math. 62 (1980) 113--141. (with I.P.Goulden)
84. An algebraic theory of sequence enumeration, J. Combinatorial Theory (A) 28 (1980) 191--218. (with B. Jeffcott and W.T.Spears)
85. The enumeration of sequences with respect to structures on a bipartition, Discrete Math., 28 (1980) 133--149. (with B.Jeffcott and W.T.Spears)

    1979

86. A formal calculus for the enumerative system of sequences - II. Applications, Studies Appl. Math. 61 (1979) 245--277. (with I.P.Goulden)
87. A formal calculus for the enumerative system of sequences - I. Combinatorial Theorems, Studies Appl. Math. 61 (1979) 141--178. (with I.P.Goulden)
88. An inversion theorem for cluster decompositions with distinguished subsequences, J. London Math. Soc. 20 (1979) 567--576. (with I.P.Goulden)
89. Sequence enumeration and the de Bruijn, van Aardenne-Ehrenfest, Smith, Tutte theorem, Canad. J. Math. 31 (1979) 488--495. (with I.P.Goulden)
90. The application of algebraic methods to the enumeration of sequences and their q-analogues, Ars Combinatoria 8 (1979) 13--18. (with I.P.Goulden)

    1978

91. Some results on product weighted lead codes, J. Combinatorial Theory (A) 25 (1978) 181--187.
92. A note on permutations without runs of given length, Aequat. Math. 17 (1978) 336-343. (with R.C.Read)
93. The enumeration of generalised alternating subsets with congruences, Discrete Math. 22 (1978) 99--104. (with I.P.Goulden)

    1977

94. The combinatorial interpretation of the Jacobi Identity from Lie algebras, J. Combinatorial Theory (A) 23 (1977) 23--256.
95. Decomposition based generating functions for sequences, Canad. J. Math. 77 (1977) 971--1009. (with R. Aleliunas)
96. The unification of certain enumeration problems for sequences, J. Combinatorial Theory (A) 22 (1977) 92--96.

    1976

97. Laguerre polynomials and derangements, Math. Proc. Camb. Philos. Soc. 80 (1976) 213-214.
98. Permutations with a prescribed number of p-runs, Ars Combinatoria 1 (1976) 297--305. (with J.W.Reilly)

    1975

99. The enumeration of homeomorphically irreducible labelled graphs, J. Combinatorial Theory 19 (1975) 272--286. (with J.W.Reilly)
100. The enumeration of doubly stochastic non-negative integer square matrices, SIAM J. Comput. 4 (1975) 474--477. (with G.H.J. van Rees)

     1973

101. Closed form approximations for random errors in distance functions, Computer J. 16 (1973) 52-56.

     1972

102. Expectations of functions of sequences over finite alphabets with given transition probabilities by methods independent of sequence length, SIAM J. Computing 1 (1972) 203--217.