Publications

Publications are listed chronologically by date of publication. Papers which have been accepted or submitted appear at the end of the list.

  1. S. Milne. Restricted growth functions and incidence relations of the lattice of partitions on an $n$-set. Advances in Mathematics 26 (1977), 290-305.
  2. S. Milne and J. Lepowsky. Lie algebras and classical partition identities, Proceedings of the National Academy of Sciences, U.S.A. 75 (1978), 578-579.
  3. S. Milne and J. Lepowsky. Lie algebraic approaches to classical partition identities, Advances in Mathematics 29 (1978), 15-59.
  4. S. Milne. A $q$-analog of restricted growth functions, Dobinski's equality, and Charlier polynomials, Transactions of the American Mathematical Society 245 (1978), 89-118.
  5. S. Milne. Peano curves and smoothness of functions, Advances in Mathematics 35 (1980), 129-157.
  6. S. Milne. Hypergeometric series well-poised in $SU(n)$ and generalization of Biedenharn's $G$-functions, Advances in Mathematics 36 (1980), 169-211.
  7. S. Milne, L. Biedanharn and W. Holman III. The invariant polynomials characterizing $U(n)$ tensor operators $$ having maximal null space, Advances in Applied Mathematics 1 (1980), 390-472.
  8. S. Milne. A multiple series transformation of the very well-poised $_{2k+4}\Psi_{2k+4}$, Pacific Journal of Mathematics 91 (1980), 419-430.
  9. S. Milne. Inversion properties of triangular arrays of numbers, International Journal of Analysis and its Applications 1 (1981), 1-7.
  10. S. Milne and A. Garsia. A method for constructing bijections for classical partition identities, Proceedings of the National Academy of Sciences, U.S.A. 78 (1981), 2026-2028.
  11. S. Milne and A. Garsia. A Rogers-Ramanujan Bijection, Journal of Combinatorial Theory (Series A) 31 (1981), 289-339.
  12. S. Milne. Restricted growth functions, rank row matchings of partition lattices, and $q$-Stirling numbers, Advances in Mathematics 43 (1982), 173-196.
  13. S. Milne. Mappings of subspaces into subsets, Journal of Combinatorial Theory (Series A) 33 (1982), 36-47.
  14. S. Milne. A generalization of Andrews' reduction formula for the Roger-Selberg functions, American Journal of Mathematics 104 (1982), 635-643.
  15. S. Milne and R. Gustafson. Schur functions and the invariant polynomials characterizing $U(n)$ tensor operators, Advances in Applied Mathematics 4 (1983), 422-478.
  16. S. Milne and R. Gustafson. Schur functions, Good's identity, and hypergeometric series well-poised in $SU(n)$, Advances in Mathematics 48 (1983), 177--188.
  17. S. Milne, L. Biedenharn and R. Gustafson. An umbral calculus for polynomials characterizing $U(n)$ tensor operators, Advances in Mathematics 51 (1984), 36-90.
  18. S. Milne, L. Biedenharn, R. Gustafson, M. Lohe and J. Louck. Special functions and group theory in theoretical physics, in ``Special Functions. Group Theoretical Aspects and Applications'' (R. A. Askey, T. H. Koornwinder, W. Schempp, Editors), pp. 129-162. D. Reidel, Dordrecht, 1984.
  19. S. Milne, A $q$-analog of the $_5F_4(1)$ summation theorem for hypergeometric series well-poised in $SU(n)$, Advances in Mathematics 57 (1985), 14-33.
  20. S. Milne. An elementary proof of the Macdonald identities for $A^{(1)}_l$, Advances in Mathematics 57 (1985), 34-70.
  21. S. Milne. A new symmetry related to $SU(n)$ for classical basic hypergeometric series, Advances in Mathematics 57 (1985), 71-90.
  22. S. Milne and R. Gustafson. A new symmetry for Biedenharn's $G$-functions and classical hypergeometric series, Advances in Mathematics 57 (1985), 209-225.
  23. S. Milne. A $q$-analog of hypergeometric series well-poised in $SU(n)$ and invariant $G$-functions, Advances in Mathematics 58 (1985), 1-60.
  24. S. Milne, L. Biedenharn and R. Gustafson. $U(n)$ Wigner coefficients, the path sum formula and invariant $G$-functions, Advances in Applied Mathematics 6 (1985), 291-349.
  25. S. Milne and R. Gustafson. A $q$-analog of transposition symmetry for invariant $G$-functions, Journal of Mathematical Analysis and Applications 114 (1986), 210-240.
  26. S. Milne. A $U(n)$ generalization of Ramanujan's $_1\Psi_1$ summation, Journal of Mathematical Analysis and Applications 118 (1986), 263-277.
  27. S. Milne. Basic hypergeometric series very well-poised in $U(n)$, Journal of Mathematical Analysis and Applications 122 (1987), 223-256.
  28. S. Milne. A $q$-analog of the Gauss summation theorem for hypergeometric series in $U(n)$, Advances in Mathematics 72 (1988), 59-131.
  29. S. Milne. Multiple $q$-series and $U(n)$ generalizations of Ramanujan's $_1\Psi_1$ sum, in ``Ramanujan Revisited'' (G.E. Andrews, R.A. Askey, B.C. Berndt, K.G. Ramanathan, R.A. Rankin, Editors), pp. 473-524. Academic Press, Boston, 1988.
  30. S. Milne. The multidimensional $_1\Psi_1$ sum and Macdonald identities for $A^{(1)}_l$, Proceedings of Symposia in Pure Mathematics, 49 (Part 2) (1989), 323-359.
  31. S. Milne. A triple product identity for Schur functions, Journal of Mathematical Analysis and Applications 160 (1991), 446-458.
  32. S. Milne and G. Lilly. The $A_\elll$ and $C_\ell$ Bailey transform and lemma, American Mathematical Society. Bulletin. New Series. 26 (1992), 258-263.
  33. S. Milne. Classical partition functions and the $U(n+1)$ Rogers-Selberg identity, Discrete Mathematics 99 (1992), 199-246.
  34. S. Milne, Summation theorems for basic hypergeometric series of Schur function argument, in ``Progress in Approximation Theory'' (A. A. Gonchar and E. B. Saff, Editors), pp. 51-77. Springer-Verlag, New York,1992.
  35. S. Milne. A $q$-analog of the balanced $_3F_2$ summation theorem for hypergeometric series in $U(n)$, Advances in Mathematics 99 (1993), 162-237.
  36. S. Milne and G. Lilly. The $C_\ell$ Bailey transform and Bailey lemma, Constructive Approximation 9 (1993), 473-500.
  37. S. Milne. A $q$-analog of a Whipple's transformation for hypergeometric series in $U(n)$, Advances in Mathematics 108 (1994), 1-76.
  38. S. Milne. The $C_\ell$ Rogers-Selberg Identity, SIAM Journal on Mathematical Analysis 25 (1994), 571-595.
  39. S. Milne and G. Lilly. Consequences of the $A_\ell$ and $C_\ell$ Bailey transform and Bailey lemma, Discrete Mathematics 139 (1995), 319-346.
  40. S. Milne and J. W. Newcomb. U(n) very well-poised $_{10}\phi_9$ transformations, Journal of Computational and Applied Mathematics 68 (1996), 239-285.
  41. S. Milne, New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan's tau function, Proceedings of the National Academy of the Sciences 93 (Number 26) (December 1996), 15004-15008. (PNAS online reprint)
  42. Stephen C. Milne, ``New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan's tau function'', pp. 403 - 417 of Formal Power Series and Algebraic Combinatorics, 9th Conference, July 14 - July 18, 1997, Universität Wien, Conference Proceedings -- Volume 3 of 3. (eds.: P. Kirschenhofer, C. Krattenthaler, D. Krob, and H. Prodinger), FPSAC'97 (1997). (FPSAC'97 paper)
  43. S. Milne. Balanced $_3\phi_2$ summation theorems for $U(n)$ basic hypergeometric series, Advances in Mathematics 131 (1997), 93-187.
  44. S. Milne and G. Bhatnagar. Generalized bibasic hypergeometric series and their $U(n)$ extensions, Advances in Mathematics 131 (1997), 188-252.
  45. S. Milne and G. Bhatnagar. A characterization of inverse relations, Discrete Mathematics 193 (1998), 235--245.
  46. S. Milne and V. Leininger. Expansions for $(q)_{\infty}^{n^2+2n}$ and basic hypergeometric series in $U(n)$, Discrete Mathematics 204 (1999), 281--317.
  47. S. Milne and V. Leininger. Some new infinite families of eta function identities, Methods and Applications of Analysis 6 (1999), 225--248.
  48. S. Milne and S. Degenhardt. Weighted-inversion statistics and their symmetry groups, Journal of Combinatorial Theory (Series A) 90 (2000), 49--103.
  49. S. Milne. A new $U(n)$ generalization of the Jacobi triple product identity, in ``$q$-Series from a Contemporary Perspective (Mount Holyoke College, South Hadley, MA, 1998)'' (M. E. H. Ismail and D. W. Stanton, Editors), vol. 254 of Contemporary Mathematics, American Mathematical Society, Providence, RI, 2000, pp. 351--370.
  50. S. Milne. Transformations of $U(n+1)$ multiple basic hypergeometric series, in ``Physics and Combinatorics: Proceedings of the Nagoya 1999 International Workshop (Nagoya University, Japan, August 23--27, 1999)'' (A. N. Kirillov, A. Tsuchiya, and H. Umemura, Editors), World Scientific, Singapore, 2001, pp. 201--243.
  51. S. Milne. Hankel determinants of Eisenstein series, in ``Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics (University of Florida, Gainesville, November 11--13, 1999)'' (F. G. Garvan and M. E. H. Ismail, Editors), vol. 4 of Developments in Mathematics, Kluwer Academic Publishers, Dordrecht, 2001, pp. 171--188.
  52. S. Milne. Infinite families of exact sums of squares formulas, Jacobi elliptic functions, continued fractions, and Schur functions, The Ramanujan Journal 6 (2002), 7--149.( Preface by George Andrews on pages 5--6.) Entire paper (issue) also published in hardcover book form as vol. 5 of ``Developments in Mathematics'', Kluwer Academic Publishers, Dordrecht, 2002. (ISBN \#1-4020-0491-5). ( Kluwer online abstract)
  53. S. Milne (with M. Schlosser) A new $A_n$ extension of Ramanujan's ${}_1\psi_{1}$ summation with applications to multilateral $A_n$ series, (In the proceedings of the ``NATO Advanced Study Institute Special Functions 2000 workshop'' held May 29--June 9, 2000 at Arizona State University, Tempe, Arizona.), Rocky Mountain J. Math. 32 (2002), 759--792.
  54. S. Milne (with E. Kolomeisky and J. Straley) The Bose molecule in one dimension, Journal of Statistical Physics 116 (2004), 1579--1596.
  55. S. Milne (with J. W. Newcomb) Nonterminating q-Whipple Transformations for Basic Hypergeometric Series in U(n), in ``Partitions, q-Series, and Modular Forms'', vol. 23 of Developments in Mathematics, Springer, New York, 2012, pp. 181—224 [Hardcover, ISBN 978-1-4614-0027-1]

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