The University of Queensland

Logarithmic and complex constant term identities

Chappell, Tom, Lascoux, Alain, Warnaar, S. Ole and Zudilin, Wadim (2013). Logarithmic and complex constant term identities. Computational and analytical mathematics. (pp. 219-250) edited by David H. Bailey, Heinz H. Bauschke, Peter Borwein, Frank Garvan, Michel Théra, Jon D. Vanderwerff and Henry Wolkowicz. New York, United States: Springer. doi: 10.1007/978-1-4614-7621-4_11

AFLT-type Selberg integrals

Albion, Seamus P., Rains, Eric M. and Warnaar, S. Ole (2021). AFLT-type Selberg integrals. Communications in Mathematical Physics, 388 (2), 735-791. doi: 10.1007/s00220-021-04157-0

A Nekrasov–Okounkov formula for Macdonald polynomials

Rains, Eric M. and Warnaar, S. Ole (2017). A Nekrasov–Okounkov formula for Macdonald polynomials. Journal of Algebraic Combinatorics, 48 (1), 1-30. doi: 10.1007/s10801-017-0790-2

Discrete analogues of Macdonald-Mehta integrals

Brent, Richard P., Krattenthaler, Christian and Warnaar, Ole (2016). Discrete analogues of Macdonald-Mehta integrals. Journal of Combinatorial Theory. Series A, 144, 80-138. doi: 10.1016/j.jcta.2016.06.005

Fifty years of The Journal of Combinatorial Theory

Barcelo, Helene, Rothschild, Bruce L. and Warnaar, S. Ole (2016). Fifty years of The Journal of Combinatorial Theory. Journal of Combinatorial Theory. Series A, 144 (3), 1-6. doi: 10.1016/j.jcta.2016.06.003

A framework of Rogers-Ramanujan identities and their arithmetic properties

Griffin, Michael J., Ono, Ken and Warnaar, S. Ole (2016). A framework of Rogers-Ramanujan identities and their arithmetic properties. Duke Mathematical Journal, 165 (8), 1475-1527. doi: 10.1215/00127094-3449994

Hall-Littlewood polynomials and characters of affine Lie algebras

Bartlett, Nick and Warnaar, S. Ole (2015). Hall-Littlewood polynomials and characters of affine Lie algebras. Advances in Mathematics, 285, 1066-1105. doi: 10.1016/j.aim.2015.08.011

Constant term identities and Poincaré polynomials

Károlyi, Gyula, Lascoux, Alain and Ole Warnaar, S. (2015). Constant term identities and Poincaré polynomials. Transactions of the American Mathematical Society, 367 (10), 6809-6836. doi: 10.1090/tran/6119

A tribute to Dick Askey

Koornwinder, Tom, Van Assche, Walter and Warnaar, Ole (2015). A tribute to Dick Askey. Journal of Approximation Theory, 193, 1-3. doi: 10.1016/j.jat.2015.03.001

Remarks on the paper "Skew Pieri rules for Hall-Littlewood functions" by Konvalinka and Lauve

Warnaar, S. Ole (2013). Remarks on the paper "Skew Pieri rules for Hall-Littlewood functions" by Konvalinka and Lauve. Journal of Algebraic Combinatorics, 38 (3), 519-526. doi: 10.1007/s10801-013-0423-3

Dedekind's eta-function and Rogers-Ramanujan identities

Warnaar, S. Ole and Zudilin, Wadim (2012). Dedekind's eta-function and Rogers-Ramanujan identities. Bulletin of the London Mathematical Society, 44 (1), 1-11. doi: 10.1112/blms/bdr019

The Riemann Hypothesis

Warnaar, Ole and Zudilin, Wadim (2011, 12 07). The Riemann Hypothesis

New multiple 6ψ6 summation formulas and related conjectures

Spiridonov, Vyacheslav P. and Warnaar, S. Ole (2011). New multiple 6ψ6 summation formulas and related conjectures. The Ramanujan Journal, 25 (3), 319-342. doi: 10.1007/s11139-011-9310-5

A q-rious positivity

Warnaar, S. Ole and Zudilin, W. (2011). A q-rious positivity. Aequationes Mathematicae, 81 (1-2), 177-183. doi: 10.1007/s00010-010-0055-9

Branching rules for symmetric Macdonald polynomials and sl_n basic hypergeometric series

Lascoux, Alain and Warnaar, S. Ole (2011). Branching rules for symmetric Macdonald polynomials and sl_n basic hypergeometric series. Advances in Applied Mathematics, 46 (1-4), 424-456. doi: 10.1016/j.aam.2010.01.012

The sl(3) Selberg integral

Warnaar, S. Ole (2010). The sl(3) Selberg integral. Advances in Mathematics, 224 (2), 499-524. doi: 10.1016/j.aim.2009.11.011

A Selberg integral for the Lie algebra An

Warnaar, S. Ole (2009). A Selberg integral for the Lie algebra An. Acta Mathematica, 203 (2), 269-304. doi: 10.1007/s11511-009-0043-x

Nonsymmetric interpolation Macdonald polynomials and gln basic hypergeometric series

Lascoux, Alain, Rains, Eric. M. and Warnaar, S. Ole (2009). Nonsymmetric interpolation Macdonald polynomials and gln basic hypergeometric series. Transformation Groups, 14 (3), 613-647. doi: 10.1007/s00031-009-9061-1

The importance of the Selberg integral

Forrester, P. J. and Warnaar, S. O. (2008). The importance of the Selberg integral. Bulletin (New Series) of the American Mathematical Society, 45 (4), 489-534. doi: 10.1090/S0273-0979-08-01221-4

Bisymmetric functions, Macdonald polynomials and sl3 basic hypergeometric series

Warnaar, S. O. (2008). Bisymmetric functions, Macdonald polynomials and sl3 basic hypergeometric series. Compositio Mathematica, 144 (02), 271-303. doi: 10.1112/S0010437X07003211

On the generalised Selberg integral of Richards and Zheng

Warnaar, S. O. (2008). On the generalised Selberg integral of Richards and Zheng. Advances in Applied Mathematics, 40 (2), 212-218. doi: 10.1016/j.aam.2006.12.002

Characters of graded parafermion conformal field theory

Fortin, J. F., Mathieu, P. and Warnaar, S. O. (2007). Characters of graded parafermion conformal field theory. Advances in Theoretical and Mathematical Physics, 11 (6), 945-989.

Proof of the Flohr-Grabow-Koehn conjectures for characters of logarithmic conformal field theory

Warnaar, S. O. (2007). Proof of the Flohr-Grabow-Koehn conjectures for characters of logarithmic conformal field theory. Journal Of Physics A-Mathematical And Theoretical, 40 (40), 12243-12254. doi: 10.1088/1751-8113/40/40/015

The Bailey transform and false theta functions

Andrews, G. E. and Warnaar, S. O. (2007). The Bailey transform and false theta functions. Ramanujan Journal, 14 (1), 173-188. doi: 10.1007/s11139-006-9006-4

The product of partial theta functions

Andrews, G. E. and Warnaar, S. O. (2007). The product of partial theta functions. Advances in Applied Mathematics, 39 (1), 116-120. doi: 10.1016/j.aam.2005.12.003

Inversions of integral operators and elliptic beta integrals on root systems

Vyacheslav P., Spiridonov, S. and Warnaar, S. O. (2006). Inversions of integral operators and elliptic beta integrals on root systems. Advances in Mathematics, 207 (1), 91-132. doi: 10.1016/j.aim.2005.11.007

Rogers-Szego polynomials and Hall-Littlewood symmetric functions

Warnaar, S. Ole (2006). Rogers-Szego polynomials and Hall-Littlewood symmetric functions. Journal of Algebra, 303 (2), 810-830. doi: 10.1016/j.jalgebra.2006.04.026

Hall–Littlewood functions and the A2 Rogers–Ramanujan identities

Warnaar, S. O. (2006). Hall–Littlewood functions and the A2 Rogers–Ramanujan identities. Advances in Mathematics, 200 (2), 403-434. doi: 10.1016/j.aim.2004.12.001

A generalization of the Farkas and Kra partition theorem for modulus 7

Warnaar, S. O. (2005). A generalization of the Farkas and Kra partition theorem for modulus 7. Journal of Combinatorial Theory Series A, 110 (1), 43-52. doi: 10.1016/j.jcta.2004.08.008

Positivity preserving transformations for q-binomial coefficients

Berkovich, A. and Warnaar, S. O. (2005). Positivity preserving transformations for q-binomial coefficients. Transactions of the American Mathematical Society, 357 (6), 2291-2351. doi: 10.1090/S0002-9947-04-03680-3

Summation formulae for elliptic hypergeometric series

Warnaar, S. O. (2005). Summation formulae for elliptic hypergeometric series. Proceedings of the American Mathematical Society, 133 (2), 519-527. doi: 10.1090/S0002-9939-04-07558-6

q-Hypergeometric proofs of polynomial analogues of the triple product identity, Lebesgue's identity and Euler's pentagonal number theorem

Warnaar, S. O. (2005). q-Hypergeometric proofs of polynomial analogues of the triple product identity, Lebesgue's identity and Euler's pentagonal number theorem. Ramanujan Journal, 8 (4), 467-474. doi: 10.1007/s11139-005-0275-0

The Bailey Lemma and Kostka Polynomials

Warnaar, S. O. (2004). The Bailey Lemma and Kostka Polynomials. Journal of Algebraic Combinatorics, 20 (2), 131-171. doi: 10.1023/B:JACO.0000047280.16877.1f

On the q-analogue of the sum of cubes

Warnaar, S. Ole (2004). On the q-analogue of the sum of cubes. The Electronic Journal of Combinatorics, 11 (1), N13-1-N13-2.

Extensions of the well-poised and elliptic well-poised Bailey lemma

Warnaar, S. O. (2003). Extensions of the well-poised and elliptic well-poised Bailey lemma. Indagationes Mathematicae, 14 (3-4), 571-588. doi: 10.1016/S0019-3577(03)90060-7

The generalized borwein conjecture. II. Refined q-trinomial coefficients

Warnaar, S. O. (2003). The generalized borwein conjecture. II. Refined q-trinomial coefficients. Discrete Mathematics, 272 (2-3), 215-258. doi: 10.1016/S0012-365X(03)00047-5

Partial Theta Functions. I. Beyond the Lost Notebook

Warnaar, S. O. (2003). Partial Theta Functions. I. Beyond the Lost Notebook. Proceedings of the London Mathematical Society, 87 (2), 363-395. doi: 10.1112/S002461150201403X

Partial-sum analogues of the Rogers-Ramanujan identities

Warnaar, S. O. (2002). Partial-sum analogues of the Rogers-Ramanujan identities. Journal of Combinatorial Theory, Series A, 99 (1), 143-161. doi: 10.1006/jcta.2002.3266

Hyp

Warnaar, S. O. (2002). Hyp. Australian Mathematical Society Gazette, 29 (5), 277-279.

Summation and transformation formulas for elliptic hypergeometric series

Warnaar, S. O. (2002). Summation and transformation formulas for elliptic hypergeometric series. Constructive Approximation, 18 (4), 479-502. doi: 10.1007/s00365-002-0501-6

Theta functions, elliptic hypergeometric series, and Kawanaka's Macdonald polynomial conjecture

Langer, Robin, Schlosser, Michael J. and Warnaar, S. Ole (2009). Theta functions, elliptic hypergeometric series, and Kawanaka's Macdonald polynomial conjecture. Workshop on Elliptic Integrable Systems, Isomonodromy Problems, and Hypergeometric Functions, Bonn, Germany, 21-25 Jul 2008. Kyiv, Ukraine: Natsional'na Akademiya Nauk Ukrainy. doi: 10.3842/SIGMA.2009.055

The Mukhin-Varchenko conjecture for type A

Warnaar, S. Ole (2008). The Mukhin-Varchenko conjecture for type A. FPSAC 2008: 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics, Viña del Mar, Chile, 23-27 June, 2008. Nancy, France: INRIA.

q-Selberg Integrals and Macdonald Polynomials

Warnaar, S. O. (2005). q-Selberg Integrals and Macdonald Polynomials. Conference on Number Theory and Combinatorics in Physics, Gainesville, Florida, 21-23 Mar 2003. Dordrecht, The Netherlands: Springer. doi: 10.1007/s11139-005-4849-7

Conjugate Bailey pairs. From configuration sums and fractional-level string functions to Bailey's lemma

Schilling , A. and Warnaar, S. O. (2002). Conjugate Bailey pairs. From configuration sums and fractional-level string functions to Bailey's lemma. Recent Developments in Infinite-Dimensional Lie Algebras and Conformal Field Theory, Charlottesville, Virginia, USA, 23 - 27 may 2000. American Mathematical Society.

Counting Complexity: An International Workshop on Statistical Mechanics and Combinatorics

Jan de Gier and Ole Warnaar eds. (2006). Counting Complexity: An International Workshop on Statistical Mechanics and Combinatorics. Counting Complexity: An International Workshop on Statistical Mechanics and Combinatorics, Dunk Island, Queensland, Australia, 10–15 July 2005.