The University of Queensland

Elliptic hypergeometric functions associated with root systems

Rosengren, H. and Warnaar, S. O. (2020). Elliptic hypergeometric functions associated with root systems. Encyclopedia of special functions: the Askey-Bateman Project. (pp. 159-186) Cambridge, United Kingdom: Cambridge University Press. doi: 10.1017/9780511777165.007

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

Bounded Littlewood identities

Rains, Eric M. and Warnaar, S. Ole (2021). Bounded Littlewood identities. Memoirs of the American Mathematical Society, 270 (1317), 1-115. doi: 10.1090/memo/1317

An elliptic hypergeometric function approach to branching rules

Lee, Chul-Hee, Rains, Eric M. and Warnaar, S. Ole (2020). An elliptic hypergeometric function approach to branching rules. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 16 142, 1-52. doi: 10.3842/SIGMA.2020.142

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

Srinivasa Ramanujan: Going Strong at 125, Part II

Alladi, Krishnaswami, Ono, Ken, Soundararajan, K., Vaughan, R. C. and Warnaar, S. Ole (2013). Srinivasa Ramanujan: Going Strong at 125, Part II. Notices of the American Mathematical Society, 60 (01), 10-22. doi: 10.1090/noti926

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

Refined q-trinomial coefficients and character identities

Warnaar, SO (2001). Refined q-trinomial coefficients and character identities. Journal of Statistical Physics, 102 (3-4), 1065-1081. doi: 10.1023/A:1004827709169

An A(2) Bailey lemma and Rogers-Ramanujan-type identities

Andrews, GE, Schilling, A and Warnaar, SO (1999). An A(2) Bailey lemma and Rogers-Ramanujan-type identities. Journal of the American Mathematical Society, 12 (3), 677-702. doi: 10.1090/S0894-0347-99-00297-0

q-trinomial identities

Warnaar, SO (1999). q-trinomial identities. Journal of Mathematical Physics, 40 (5), 2514-2530. doi: 10.1063/1.532880

Inhomogeneous lattice paths, generalized Kostka polynomials and A(n-1) supernomials

Schilling, A and Warnaar, SO (1999). Inhomogeneous lattice paths, generalized Kostka polynomials and A(n-1) supernomials. Communications in Mathematical Physics, 202 (2), 359-401. doi: 10.1007/s002200050586

A higher level Bailey lemma: Proof and application

Schilling, A and Warnaar, SO (1998). A higher level Bailey lemma: Proof and application. Ramanujan Journal, 2 (3), 327-349. doi: 10.1023/A:1009746932284

A note on the trinomial analogue of Bailey's lemma

Warnaar, SO (1998). A note on the trinomial analogue of Bailey's lemma. Journal of Combinatorial Theory Series a, 81 (1), 114-118. doi: 10.1006/jcta.1997.2830

Supernomial coefficients, polynomial identities and q-series

Schilling, A and Warnaar, SO (1998). Supernomial coefficients, polynomial identities and q-series. Ramanujan Journal, 2 (4), 459-494. doi: 10.1023/A:1009780810189

Analytic calculation of conformal partition functions: Tricritical hard squares with fixed boundaries

OBrien, DL, Pearce, PA and Warnaar, SO (1997). Analytic calculation of conformal partition functions: Tricritical hard squares with fixed boundaries. Nuclear Physics B, 501 (3), 773-799. doi: 10.1016/S0550-3213(97)00424-0

Bailey flows and Bose-Fermi identities for the conformal coset models (A(1)((1)))(N) x (A(1)((1)))(N')/(A(1)((1)))(N+N')

Berkovich, A, McCoy, BM, Schilling, A and Warnaar, SO (1997). Bailey flows and Bose-Fermi identities for the conformal coset models (A(1)((1)))(N) x (A(1)((1)))(N')/(A(1)((1)))(N+N'). Nuclear Physics B, 499 (3), 621-649. doi: 10.1016/S0550-3213(97)82955-0

The Andrews-Gordon identities and q-multinomial coefficients

Warnaar, SO (1997). The Andrews-Gordon identities and q-multinomial coefficients. Communications in Mathematical Physics, 184 (1), 203-232. doi: 10.1007/s002200050058

Fermionic solution of the Andrews-Baxter-Forrester model .2. Proof of Melzer's polynomial identities

Warnaar, SO (1996). Fermionic solution of the Andrews-Baxter-Forrester model .2. Proof of Melzer's polynomial identities. Journal of Statistical Physics, 84 (1-2), 49-83. doi: 10.1007/BF02179577

Finitized conformal spectrum of the Ising model on the cylinder and torus

OBrien, DL, Pearce, PA and Warnaar, SO (1996). Finitized conformal spectrum of the Ising model on the cylinder and torus. Physica a, 228 (1-4), 63-77. doi: 10.1016/S0378-4371(96)00055-6

A bijection which implies Melzer's polynomial identities: The chi(1,1)((p,p+1)) case

Foda, O and Warnaar, SO (1996). A bijection which implies Melzer's polynomial identities: The chi(1,1)((p,p+1)) case. Letters in Mathematical Physics, 36 (2), 145-155. doi: 10.1007/BF00714377

A proof of polynomial identities of type s(l(n))over-cap(1)circle times s(l(n))over-cap(1)/s(l(n))over-cap(2)

Foda, O, Okado, M and Warnaar, SO (1996). A proof of polynomial identities of type s(l(n))over-cap(1)circle times s(l(n))over-cap(1)/s(l(n))over-cap(2). Journal of Mathematical Physics, 37 (2), 965-986. doi: 10.1063/1.531698

Yang-Baxter algebras based on the two-colour BWM algebra

Grimm, U and Warnaar, SO (1995). Yang-Baxter algebras based on the two-colour BWM algebra. Journal of Physics A-Mathematical and General, 28 (24), 7197-7207. doi: 10.1088/0305-4470/28/24/017

ALGEBRAIC CONSTRUCTION OF HIGHER-RANK DILUTE A-MODELS

WARNAAR, SO (1995). ALGEBRAIC CONSTRUCTION OF HIGHER-RANK DILUTE A-MODELS. Nuclear Physics B, 435 (3), 463-481. doi: 10.1016/0550-3213(94)00424-D

SOLVABLE RSOS MODELS BASED ON THE DILUTE BWM ALGEBRA

GRIMM, U and WARNAAR, SO (1995). SOLVABLE RSOS MODELS BASED ON THE DILUTE BWM ALGEBRA. Nuclear Physics B, 435 (3), 482-504. doi: 10.1016/0550-3213(94)00405-4

EXCEPTIONAL STRUCTURE OF THE DILUTE A(3) MODEL - E(8) AND E(7) ROGERS-RAMANUJAN IDENTITIES

WARNAAR, SO and PEARCE, PA (1994). EXCEPTIONAL STRUCTURE OF THE DILUTE A(3) MODEL - E(8) AND E(7) ROGERS-RAMANUJAN IDENTITIES. Journal of Physics A-Mathematical and General, 27 (23), L891-L897. doi: 10.1088/0305-4470/27/23/005

LATTICE ISING-MODEL IN A FIELD - E8 SCATTERING-THEORY

BAZHANOV, VV, NIENHUIS, B and WARNAAR, SO (1994). LATTICE ISING-MODEL IN A FIELD - E8 SCATTERING-THEORY. Physics Letters B, 322 (3), 198-206. doi: 10.1016/0370-2693(94)91107-X

ORDER PARAMETERS OF THE DILUTE A-MODELS

WARNAAR, SO, PEARCE, PA, SEATON, KA and NIENHUIS, B (1994). ORDER PARAMETERS OF THE DILUTE A-MODELS. Journal of Statistical Physics, 74 (3-4), 469-531. doi: 10.1007/BF02188569

SOLVABLE LATTICE MODELS LABELED BY DYNKIN DIAGRAMS

WARNAAR, SO and NIENHUIS, B (1993). SOLVABLE LATTICE MODELS LABELED BY DYNKIN DIAGRAMS. Journal of Physics A-Mathematical and General, 26 (10), 2301-2316. doi: 10.1088/0305-4470/26/10/005

EXACT MULTICRITICAL BEHAVIOR OF THE POTTS-MODEL

NIENHUIS, B, WARNAAR, SO and BLOTE, HWJ (1993). EXACT MULTICRITICAL BEHAVIOR OF THE POTTS-MODEL. Journal of Physics A-Mathematical and General, 26 (3), 477-493. doi: 10.1088/0305-4470/26/3/013

NEW CONSTRUCTION OF SOLVABLE LATTICE MODELS INCLUDING AN ISING-MODEL IN A FIELD

WARNAAR, SO, NIENHUIS, B and SEATON, KA (1992). NEW CONSTRUCTION OF SOLVABLE LATTICE MODELS INCLUDING AN ISING-MODEL IN A FIELD. Physical Review Letters, 69 (5), 710-712. doi: 10.1103/PhysRevLett.69.710

CRITICAL PROPERTIES OF THE IZERGIN-KOREPIN AND SOLVABLE O(N) MODELS AND THEIR RELATED QUANTUM SPIN CHAINS

WARNAAR, SO, BATCHELOR, MT and NIENHUIS, B (1992). CRITICAL PROPERTIES OF THE IZERGIN-KOREPIN AND SOLVABLE O(N) MODELS AND THEIR RELATED QUANTUM SPIN CHAINS. Journal of Physics A-Mathematical and General, 25 (11), 3077-3095. doi: 10.1088/0305-4470/25/11/016

BETHE-ANSATZ RESULTS FOR A SOLVABLE O(N) MODEL ON THE SQUARE LATTICE

BATCHELOR, MT, NIENHUIS, B and WARNAAR, SO (1989). BETHE-ANSATZ RESULTS FOR A SOLVABLE O(N) MODEL ON THE SQUARE LATTICE. Physical Review Letters, 62 (21), 2425-2428. doi: 10.1103/PhysRevLett.62.2425

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.

50 years of Bailey's lemma

Warnaar, SO (2001). 50 years of Bailey's lemma. Euroconference on Algebraic Combinatorics and Applications (Alcoma99), Grossweinstein Germany, Sep 12-19, 1999. BERLIN: SPRINGER-VERLAG BERLIN.

A generalization of the q-Saalschutz sum and the Burge transform

Schilling, A and Warnaar, SO (2000). A generalization of the q-Saalschutz sum and the Burge transform. Workshop on Physical Combinatorics, Kyoto Japan, Feb 01-02, 1999. CAMBRIDGE: BIRKHAUSER BOSTON.

A higher-level Bailey lemma

Schilling, A and Warnaar, SO (1997). A higher-level Bailey lemma. Proceedings of the Conference on Exactly Soluble Models in Statistical Mechanics - Current Status and Historical Perspectives, Boston Ma, Mar, 1996. SINGAPORE: WORLD SCIENTIFIC PUBL CO PTE LTD. doi: 10.1142/S0217979297000253

A CRITICAL ISING-MODEL IN A MAGNETIC-FIELD

WARNAAR, SO, NIENHUIS, B and SEATON, KA (1993). A CRITICAL ISING-MODEL IN A MAGNETIC-FIELD. Conf On Yang-Baxter Equations in Paris, Paris France, Jul 24-30, 1992. SINGAPORE: WORLD SCIENTIFIC PUBL CO PTE LTD. doi: 10.1142/S0217979293003474

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.