Publications


Preprints

1 H. Rosengren and S.O. Warnaar
Elliptic hypergeometric functions associated with root systems
This is a draft of the upcoming chapter on multivariable elliptic hypergeometric functions for Volume 2 of the Askey–Bateman project. Comments are welcome.
2 E.M. Rains and S.O. Warnaar
A Nekrasov–Okounkov formula for Macdonald polynomials
3 E.M. Rains and S.O. Warnaar
Bounded Littlewood identities
4 S.O. Warnaar
The A(2)2n Rogers–Ramanujan identities
Superseded by the Griffin–Ono–Warnaar paper.

Miscellany

4 H. Barcelo, B. L. Rothschild and S.O. Warnaar
Fifty years of The Journal of Combinatorial Theory
Journal of Combinatorial Theory A 144 (2016), 1–6.
3 T.H. Koornwinder, W. Van Assche and S.O. Warnaar
A tribute to Dick Askey
Journal of Approximation Theory 193 (2015), 1–3.
2 S.O. Warnaar and W. Zudilin
The Riemann Hypothesis
The Conversation, 7 December 2011.
Part of a series of short popular articles on the Millennium Prize Problems.
1 S.O. Warnaar
Hyp
Australian Mathematical Society Gazette 29 (2002), 277–279.
A short article on how to avoid rediscovering the Chu–Vandermonde sum more than 700 years after Chu Shih–Chieh.

Books

1 J. de Gier and S.O. Warnaar, Editors
Counting Complexity: An International Workshop on Statistical Mechanics and Combinatorics
Journal of Physics: Conference Series 42 (2006), 299 pages.

Published Papers

73 R.P Brent, C. Krattenthaler and S.O. Warnaar
Discrete analogues of Macdonald–Mehta integrals
Journal of Combinatorial Theory A 144 (2016), 80–138.
72 M.J. Griffin, K. Ono and S.O. Warnaar
A framework of Rogers–Ramanujan identities and their arithmetic properties
Duke Mathematical Journal 165 (2016), 1475–1527.
71 N. Bartlett and S.O. Warnaar
Hall–Littlewood polynomials and characters of affine Lie algebras
Advances in Mathematics 285 (2015), 1066–1105.
70 G. Károlyi, A. Lascoux and S.O. Warnaar
Constant term identities and Poincaré polynomials
Transactions of the American Mathematical Society 367 (2015), 6809–6836.
69 T. Chappell, A. Lascoux, S.O. Warnaar and W. Zudilin
Logarithmic and complex constant term identities
Computational and Analytical Mathematics, D.H. Bailey et al. (eds.), Springer Proceedings in Mathematics and Statistics, Volume 50, (2013), 219–250.
68 S.O. Warnaar
Remarks on the paper "Skew Pieri rules for Hall–Littlewood functions" by Konvalinka and Lauve
Journal of Algebraic Combinatorics 38 (2013), 519–526.
67 S.O. Warnaar
Ramanujan’s 1ψ1 summation
Notices of the AMS, 60, Number 1 (2013), 18–22.

Alternatively, there is the full 7.5Mb article
Srinivasa Ramanujan: Going strong at 125, Part II
Notices of the AMS, 60, Number 1 (2013), 10–22.
66 S.O. Warnaar and W. Zudilin
Dedekind’s eta-function and Rogers–Ramanujan identities
Bulletin of the London Mathematical Society 44 (2012), 1–11.
65 V.P. Spiridonov and S.O. Warnaar
New multiple 6ψ6 summation formulas and related conjectures
The Ramanujan Journal 25 (2011), 319–342.
64 S.O. Warnaar and W. Zudilin
A q-rious positivity
Aequationes Mathematicae 81 (2011), 177–183.
63 A. Lascoux and S.O. Warnaar
Branching rules for symmetric Macdonald polynomials and sln basic hypergeometric series
Advances in Applied Mathematics 46 (2011), 424–456.
62 S.O. Warnaar
The sl3 Selberg integral
Advances in Mathematics 224 (2010), 499–524.
61 S.O. Warnaar
A Selberg integral for the Lie algebra An
Acta Mathematica 203 (2009), 269–304.
60 A. Lascoux, E.M. Rains and S.O. Warnaar
Nonsymmetric interpolation Macdonald polynomials and gln basic hypergeometric series
Transformation Groups 14 (2009), 613–647.
59 R. Langer, M.J. Schlosser and S.O. Warnaar
Theta functions, elliptic hypergeometric series, and Kawanaka’s Macdonald polynomial conjecture
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 5 (2009), 055, 20 pages.
58 S.O. Warnaar
The Mukhin–Varchenko conjecture for type A
20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), DMTCS Proceedings (2008).
57 P.J. Forrester and S.O. Warnaar
The importance of the Selberg integral
Bulletin of the American Mathematical Society (New Series) 45 (2008), 489–534.
56 S.O. Warnaar
Bisymmetric functions, Macdonald polynomials and sl3 basic hypergeometric series
Compositio Mathematica 144 (2008), 271–303.
55 S.O. Warnaar
On the generalised Selberg integral of Richards and Zheng
Advances in Applied Mathematics 40 (2008), 212–218.
54 S.O. Warnaar
Proof of the Flohr–Grabow–Koehn conjectures for characters of logarithmic conformal field theory
Journal of Physics A: Mathematical and Theoretical 40 (2007), 12243–12254.
53 G.E. Andrews and S.O. Warnaar
The Bailey transform and false theta functions
The Ramanujan Journal 14 (2007), 173–188.
52 G.E. Andrews and S.O. Warnaar
The product of partial theta functions
Advances in Applied Mathematics 39 (2007), 116–120.
51 J.-F. Fortin, P. Mathieu and S.O. Warnaar
Characters of graded parafermion conformal field theory
Advances in Theoretical and Mathematical Physics 11 (2007), 945–989.
50 V.P. Spiridonov and S.O. Warnaar
Inversions of integral operators and elliptic beta integrals on root systems
Advances in Mathematics 207 (2006), 91–132.
49 S.O. Warnaar
Rogers–Szegő polynomials and Hall–Littlewood symmetric functions
Journal of Algebra 303 (2006), 810–830.
48 S.O. Warnaar
Hall–Littlewood functions and the A2 Rogers–Ramanujan identities
Advances in Mathematics 200 (2006), 403–434.
47 S.O. Warnaar
q-Selberg integrals and Macdonald polynomials
The Ramanujan Journal 10 (2005), 237–268.
46 S.O. Warnaar
A generalization of the Farkas and Kra partition theorem for modulus 7
Journal of Combinatorial Theory A 110 (2005), 43–52.
45 S.O. Warnaar
Summation formulae for elliptic hypergeometric series
Proceedings of the American Mathematical Society 133 (2005), 519–527.
44 A. Berkovich and S.O. Warnaar
Positivity preserving transformations for q-binomial coefficients
Transactions of the American Mathematical Society 357 (2005), 2291–2351.
43 S.O. Warnaar
q-Hypergeometric proofs of polynomial analogues of the triple product identity, Lebesgue’s identity and Euler’s pentagonal number theorem
The Ramanujan Journal 8 (2004), 467–474.
42 S.O. Warnaar
The Bailey lemma and Kostka polynomials
Journal of Algebraic Combinatorics 20 (2004), 131–171.
41 S.O. Warnaar
On the q-analogue of the sum of cubes
Electronic Journal of Combinatorics 11 (2004), N13.
40 S.O. Warnaar
Extensions of the well-poised and elliptic well-poised Bailey lemma
Indagationes Mathematicae, New Series 14 (2003), 571–588.
39 S.O. Warnaar
The generalized Borwein conjecture. II. Refined q-trinomial coefficients
Discrete Mathematics 272 (2003), 215–258.
38 S.O. Warnaar
Partial theta functions. I. Beyond the lost notebook
Proceedings of the London Mathematical Society 87 (2003), 363–395.
37 S.O. Warnaar
Partial-sum analogues of the Rogers–Ramanujan identities
Journal of Combinatorial Theory A 99 (2002), 143–161.
36 S.O. Warnaar
Summation and transformation formulas for elliptic hypergeometric series
Constructive Approximation 18 (2002), 479–502.
35 A. Schilling and S.O. Warnaar
Conjugate Bailey pairs. From configuration sums and fractional-level string functions to Bailey’s lemma
Contemporary Mathematics 297 (2002), 227–255.
34 S.O. Warnaar
The generalized Borwein conjecture. I. The Burge transform
Contemporary Mathematics 291 (2001), 243–267.
33 S.O. Warnaar
50 Years of Bailey’s lemma
in Algebraic Combinatorics and Applications, pp. 333–347, A. Betten et al. eds., (Springer, Berlin, 2001).
32 S.O. Warnaar
Refined q-trinomial coefficients and character identities
Journal of Statistical Physics 102 (2001), 1065–1081.
31 A. Schilling and S.O. Warnaar
A generalization of the q-Saalschütz sum and the Burge transform
in Physical Combinatorics, pp. 163–183, M. Kashiwara and T. Miwa eds., Progress in Mathematics 191, (Birkhäuser, Boston, 2000).
34 S.O. Warnaar
Supernomial coefficients, Bailey’s lemma and Rogers–Ramanujan-type identities. A survey of results and open problems
Séminaire Lotharingien de Combinatoire 42 (1999), Art. B42n 22p.
29 S.O. Warnaar
q-Trinomial identities
Journal of the Mathematical Physics 40 (1999), 2514–2530.
28 G.E. Andrews, A. Schilling, and S.O. Warnaar
An A2 Bailey lemma and Rogers–Ramanujan-type identities
Journal of the American Mathematical Society 12 (1999), 677–702.
27 A. Schilling and S.O. Warnaar
Inhomogeneous lattice paths, generalized Kostka polynomials and An-1 supernomials
Communications in Mathematical Physics 202 (1999), 359–401.
26 A. Schilling and S.O. Warnaar
Supernomial coefficients, polynomial identities and q-series
The Ramanujan Journal 2 (1998), 459–494.
25 A. Schilling and S.O. Warnaar
A higher level Bailey lemma: proof and application
The Ramanujan Journal 2 (1998), 327–349.
24 S.O. Warnaar
A note on the trinomial analogue of Bailey’s lemma
Journal of Combinatorial Theory A 81 (1998), 114–118.
23 D.L. O’Brien, P.A. Pearce and S.O. Warnaar
Analytic calculation of conformal partition functions: Tricritical hard squares with fixed boundaries
Nuclear Physics B 501 [FS] (1997), 773–799.
22 A. Berkovich, B. M. McCoy, A. Schilling and S.O. Warnaar
Bailey flows and Bose–Fermi identities for the conformal coset models (A1(1))N × (A1(1))N' / (A1(1))N+N'
Nuclear Physics B 499 [PM] (1997), 621–649.
21 S.O. Warnaar
The Andrews–Gordon identities and q-multinomial coefficients
Communications in Mathematical Physics 184 (1997), 203–232.
20 A. Schilling and S.O. Warnaar
A higher-level Bailey lemma
International Journal of Modern Physics B 11 (1997), 189–195.
19 P.A. Pearce D.L. O’Brien, and S.O. Warnaar
Finitized conformal spectrum of the Ising model on the cylinder and torus
Physica A 228 (1996), 63–77.
18 S.O. Warnaar
Fermionic solution of the Andrews–Baxter–Forrester model. II. Proof of Melzer’s polynomial identities
Journal of Statistical Physics 84 (1996), 49–83.
17 S.O. Warnaar
Fermionic solution of the Andrews–Baxter–Forrester model. I. Unification of CTM and TBA methods
Journal of Statistical Physics 82 (1996), 657–685.
16 O. Foda, M. Okado and S.O. Warnaar
A proof of polynomial identities of type sl(n)1 ⊗ sl(n)1 / sl(n)2
Journal of Mathematical Physics 37 (1996), 965–986.
15 O. Foda, and S.O. Warnaar
A bijection which implies Melzer’s polynomial identities: the χ 1,1(p,p+1)case
Letters in Mathematical Physics 36 (1996), 145–155.
14 S.O. Warnaar and P.A. Pearce
A-D-E polynomial and Rogers–Ramanujan identities
International Journal of Modern Physics A 11 (1996), 291–311.
13 U. Grimm and S.O. Warnaar
Yang–Baxter algebras based on the two-colour BWM algebra
Journal of Physics A 28 (1995), 7197–7207.
12 U. Grimm and S.O. Warnaar
Solvable RSOS models based on the dilute BWM algebra
Nuclear Physics B 435 [FS] (1995), 482–504.
11 S.O. Warnaar
Algebraic construction of higher-rank dilute A models
Nuclear Physics B 435 [FS] (1995), 463–481.
10 S.O. Warnaar and P.A. Pearce
Exceptional structure of the dilute A3 model: E8 and E7 Rogers–Ramanujan identities
Journal of Physics A 27 (1994), L891–L897.
9 V.V. Bazhanov, B. Nienhuis and S.O. Warnaar
Lattice Ising model in a field: E8 scattering theory
Physics Letters B 332 (1994), 198–206.
8 S.O. Warnaar, P.A. Pearce, B. Nienhuis and K.A. Seaton
Order parameters of the dilute A models
Journal of Statistical Physics 74 (1994), 469–531.
7 S.O. Warnaar, B. Nienhuis and K.A. Seaton
A critical Ising model in a magnetic field
International Journal of Modern Physics B7 (1993), 3727–3736.
6 S.O. Warnaar and B. Nienhuis
Solvable lattice models labelled by Dynkin diagrams
Journal of Physics A 26 (1993), 2301–2316.
5 B. Nienhuis, S.O. Warnaar and H.W.J. Blöte
Exact multicritical behaviour of the Potts model
Journal of Physics A 26 (1993), 477–493.
4 S.O. Warnaar, B. Nienhuis and K.A. Seaton
New construction of solvable lattice models including an Ising model in a field
Physical Review Letters 69 (1992), 710–712.
3 S.O. Warnaar
A tri-tricritical Potts model
Australian Mathematical Society Gazette 19 (1992), 51–57.
2 S.O. Warnaar, M.T. Batchelor and B. Nienhuis
Critical properties of the Izergin–Korepin and solvable O(n) models and their related quantum spin chains
Journal of Physics A 25 (1992), 3077–3095.
1 M.T. Batchelor, B. Nienhuis and S.O. Warnaar
Bethe Ansatz results for a solvable O(n) model on the square lattice
Physical Review Letters 62 (1989), 2425–2428.