Michael Schlosser's Home Page

Dr. Michael J. Schlosser _X
      Fakultät für Mathematik
      Universität Wien
      Oskar-Morgenstern-Platz 1
      A-1090 Wien
      Austria

telephone:	(+43-1) 4277-50455
fax:	(+43-1) 4277-850455
email:

Aktuelle Lehre.    Current Teaching.

Scientific publications (in reverse chronological order):

• Papers:
  1. Determinant evaluations inspired by Di Francesco's determinant for twenty-vertex configurations (jointly with Christoph Koutschan and Christian Krattenthaler) [37 pp.; preprint]
  2. A finite-bound partition identity generalizing a solution of a problem posed by Andrews and Deutsch (jointly with Nicolas Allen Smoot) [7 pp.; preprint]
  3. Diagonal operators, q-Whittaker functions and rook theory (jointly with Samrith Ram) [41 pp.; preprint]
  4. An elliptic extension of the multinomial theorem [14 pp.; preprint; submitted]
  5. An esoteric identity with many parameters and other elliptic extensions of elementary identities (jointly with Gaurav Bhatnagar and Archna Kumari) [New Zealand J. Math., 17 pp., to appear]
  6. Expansions of averaged truncations of basic hypergeometric series (jointly with Nian Hong Zhou) [Proc. Amer. Math. Soc., 14 pp., to appear]
  7. On an identity by Chaundy and Bullard. III. Basic and elliptic extensions (jointly with Natsuko Hoshi, Makato Katori, and Tom H. Koornwinder) [Amer. Math. Soc., Providence, R. I., Contemp. Math., 22 pp., to appear]
  8. Combinatorial formulas for Ramanujan's tau function [Srinivasa Ramanujan: His Life, Legacy, and Mathematical Influence; K. Alladi, G. E. Andrews, B. C. Berndt, F. Garvan, K. Ono, P. Paule, S. O. Warnaar, A. J. Yee (eds.), Springer, 6 pp., to appear]
  9. Supercongruences involving Domb numbers and binary quadratic forms (jointly with Guo-Shuai Mao) [Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 118, 11 (2024), 14 pp.]
  10. Lattice paths and negatively indexed weight-dependent binomial coefficients (jointly with Josef Küstner and Meesue Yoo) [Ann. Comb. 27(4) (2023), 917-955]
  11. A weighted extension of Fibonacci numbers (jointly with Gaurav Bhatnagar and Archna Kumari) [J. Difference Equ. Appl. 29(7) (2023), 733-747]
  12. Bilateral identities of the Rogers-Ramanujan type [Trans. Amer. Math. Soc. Ser. B 10 (2023), 1119-1140]
  13. Enumeration of standard barely set-valued tableaux of shifted shapes (jointly with Jang Soo Kim and Meesue Yoo) [Europ. J. Combin. 112 (2023), 103727]
  14. New q-analogues of Van Hamme's (E.2) supercongruence and of a supercongruence by Swisher (jointly with Victor J. W. Guo) [Results Math. 78 (2023), 105]
  15. Proof of a bi-symmetric septuple equidistribution on ascent sequences (jointly with Emma Yu Jin) [Combinatorial Theory 3 (1) (2023), #5, 44 pp.]
  16. Three families of q-supercongruences modulo the square and cube of a cyclotomic polynomial (jointly with Victor J. W. Guo) [Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM (2023) 117:9]
  17. An extension of a supercongruence of Long and Ramakrishna (jointly with Ji-Cai Liu and Victor J. W. Guo) [Proc. Amer. Math. Soc. 151 (2023), 1157-1166]
  18. Asymptotics and statistics on Fishburn Matrices: dimension distribution and a conjecture of Stoimenow (jointly with Hsien-Kuei Hwang and Emma Yu Jin) [Random Structures & Algorithms 62 (2) (2023), 479-518]
  19. On the infinite Borwein product raised to a positive real power (jointly with Nian Hong Zhou) [Ramanujan J. 61 (2023), 515-543]
  20. Lattice paths and negatively indexed weight-dependent binomial coefficients (jointly with Josef Küstner and Meesue Yoo) [FPSAC'22 extended abstract, Sém. Lothar. Combin. 86B (2022), Art. 86B.76, 12 pp.]
  21. A family of q-supercongruences modulo the cube of a cyclotomic polynomial (jointly with Victor J. W. Guo) [Bull. Aust. Math. Soc. 105 (2) (2022), 296-302]
  22. Bi-symmetric multiple equidistribution on ascent sequences (jointly with Emma Yu Jin) [FPSAC'21 extended abstract, Sém. Lothar. Combin. 85B (2021), Art. 85B.64, 12 pp.]
  23. Some q-supercongruences modulo the square and cube of a cyclotomic polynomial (jointly with Victor J. W. Guo) [Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 115, 132 (2021)]
  24. Log-concavity results for a biparametric and an elliptic extension of the q-binomial coefficients (jointly with Koushik Senapati and Ali K. Uncu) [Int. J. Number Th. 17(3) (2021), 787-804]
  25. Elliptic solutions of dynamical Lucas sequences (jointly with Meesue Yoo) [Entropy 2021, 23(2), 183]
  26. Some q-supercongruences from transformation formulas for basic hypergeometric series (jointly with Victor J. W. Guo) [Constr. Approx. 53 (2021), 155-200]
  27. A new family of q-supercongruences modulo the fourth power of a cyclotomic polynomial (jointly with Victor J. W. Guo) [Results Math. 75, 155 (2020)]
  28. A family of q-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial (jointly with Victor J. W. Guo) [Israel J. Math. 240 (2020), 821-835]
  29. Multidimensional matrix inversions and elliptic hypergeometric series on root systems (jointly with Hjalmar Rosengren) [SIGMA 16 (2020), 088, 21 pp.]
  30. Hypergeometric and basic hypergeometric series and integrals associated with root systems [Encyclopedia of Special Functions: The Askey-Bateman Project, ser. eds. M. E. H. Ismail and W. van Assche. Volume 2. Multivariable Special Functions, vol. eds. T. H. Koornwinder and J. Stokman, Cambridge Univ. Press, Cambridge, 2020, pp. 122-158]
  31. A noncommutative weight-dependent generalization of the binomial theorem [Sém. Lothar. Combin. 81 (2020), Art. B81j, 24 pp.]
  32. Some new q-congruences for truncated basic hypergeometric series: even powers (jointly with Victor J. W. Guo) [Results Math. 75, 1 (2020)]
  33. A tribute to Dick Askey. A small contribution to the September 2019 Richard Askey Liber Amicorum [Celebratio Mathematica, Richard Allen Askey Liber Amicorum (2022), Contribution #64, pp. 104-106]
  34. A partial theta function Borwein conjecture (jointly with Gaurav Bhatnagar) [Ann. Comb. 23(3) (2019), 561-572]
  35. Some new q-congruences for truncated basic hypergeometric series (jointly with Victor J. W. Guo) [Symmetry 2019, 11(2), 268]
  36. Proof of a basic hypergeometric supercongruence modulo the fifth power of a cyclotomic polynomial (jointly with Victor J. W. Guo) [J. Difference Equ. Appl. 25(7) (2019), 921-929]
  37. Wronskians of theta functions and series for 1/π (jointly with Alex Berkovich and Heng Huat Chan) [Adv. Math. 338 (2018), 266-304]
  38. Combinatorial interpretations of Ramanujan's tau function (jointly with Frank Garvan) [Discrete Math. 341 (2018), 2831-2840]
  39. Weight-dependent commutation relations and combinatorial identities (jointly with Meesue Yoo) [Discrete Math. 341 (2018), 2308-2325]
  40. Elliptic well-poised Bailey transforms and lemmas on root systems (jointly with Gaurav Bhatnagar) [SIGMA 14 (2018), 025, 44 pp.]
  41. Summation formulae for noncommutative hypergeometric series [in Frontiers in Orthogonal Polynomials and q-Series (Z. Nashed and X. Li, eds.), World Scientific, 2018, pp. 451-496]
  42. q-Analogues of two product formulas of hypergeometric functions by Bailey [in Frontiers in Orthogonal Polynomials and q-Series (Z. Nashed and X. Li, eds.), World Scientific, 2018, pp. 445-449]
  43. Basic hypergeometric summations from rook theory (jointly with Meesue Yoo) [in Analytic Number Theory, Modular Forms and q-Hypergeometric Series in Honor of Krishna Alladi's 60th birthday, University of Florida, Gainesville, March 2016 (G.E. Andrews and F. Garvan, eds.), Springer Proc. Math. Stat. 221 (2017), 677-692]
  44. Elliptic rook and file numbers (jointly with Meesue Yoo) [Electron. J. Combin. 24(1) (2017), #P1.31, 47 pp.]
  45. Elliptic extensions of the alpha-parameter model and the rook model for matchings (jointly with Meesue Yoo) [Adv. Appl. Math. 84 (2017), 8-33]
  46. q-Stirling numbers of the second kind and q-Bell numbers for graphs (jointly with Zsófia R. Kereskényiné Balogh) [Electronic Notes Discr. Math. 54 (2016), 361-366]
  47. Elliptic hypergeometric summations by Taylor series expansion and interpolation (jointly with Meesue Yoo) [SIGMA 12 (2016), 039, 21 pp.]
  48. An elliptic extension of the general product formula for augmented rook boards (jointly with Meesue Yoo) [Europ. J. Combin. 58 (2016), 247-266]
  49. Elliptic rook and file numbers (jointly with Meesue Yoo), DMTCS proc. FPSAC'16, 2016, 1087-1098.
  50. Some combinatorial identities involving noncommuting variables (jointly with Meesue Yoo), DMTCS proc. FPSAC'15, 2015, 961-972.
  51. The major index generating function of standard Young tableaux of shapes of the form "staircase minus rectangle" (jointly with Christian Krattenthaler) [in Ramanujan 125 (K. Alladi and F. Garvan, eds.), Amer. Math. Soc., Providence, R. I., Contemp. Math. 627 (2014), 111-122]
  52. On the work of Igor Frenkel (jointly with John Duncan, Pavel Etingof, Ivan Ip, Mikhail Khovanov, Matvei Libine, Anthony Licata, and Alistair Savage) [in Perspectives in Representation Theory (P. Etingof, M. Khovanov, and A. Savage, eds.), Amer. Math. Soc., Providence, R. I., Contemp. Math. 610 (2014), 1-21]
  53. Multiple hypergeometric series - Appell series and beyond [in Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions (J. Blümlein and C. Schneider, eds.), Texts & Monographs in Symbolic Computation, Springer-Verlag, Heidelberg/Vienna, 2013; pp. 305-324]
  54. On an identity by Chaundy and Bullard. II. More history (jointly with Tom H. Koornwinder) [Indag. Math. (N.S.) 24 (1) (2013), 174-180]
  55. New curious bilateral q-series identities (jointly with Frédéric Jouhet) [Axioms 2012, 1 (3), 365-371]
  56. Recurrence formulas for Macdonald polynomials of type A (jointly with Michel Lassalle) [J. Algebraic Combin. 32 (1) (2010), 113-131]
  57. Noncommutative hypergeometric and basic hypergeometric equations (jointly with Alessandro Conflitti) [J. Nonlinear Math. Phys. 17 (4) (2010), 429-443]
  58. Theta functions, elliptic hypergeometric series, and Kawanaka's Macdonald polynomial conjecture (jointly with Robin Langer and S. Ole Warnaar) [SIGMA 5 (2009), 055, 20 pp.]
  59. Multilateral inversion of A_r, C_r and D_r basic hypergeometric series [Ann. Comb. 13 (2009), 341-363]
  60. On an identity by Chaundy and Bullard. I (jointly with Tom H. Koornwinder) [Indag. Math. (N.S.) 19 (2) (2008), 239-261]
  61. A Taylor expansion theorem for an elliptic extension of the Askey-Wilson operator [in Special Functions and Orthogonal Polynomials (D. Dominici and R. S. Maier, eds.), Amer. Math. Soc., Providence, R. I., Contemp. Math. 471 (2008), 175-186]
  62. A new multivariable ₆ψ₆ summation formula [Ramanujan J. 17 (3) (2008), 305-319]
  63. Curious extensions of Ramanujan's ₁ψ₁ summation formula (jointly with Victor J. W. Guo) [J. Math. Anal. Appl. 334 (1) (2007), 393-403]
  64. Macdonald symmetric functions for partitions with complex parts [FPSAC'07, Nankai University, Tianjin, China, 10 pp.]
  65. Macdonald polynomials and multivariable basic hypergeometric series [Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, SIGMA 3 (2007), 056, 30 pp.]
  66. Elliptic enumeration of nonintersecting lattice paths [J. Combin. Theory Ser. A 114 (3) (2007), 505-521]
  67. Some curious q-series expansions and beta integral evaluations (jointly with George Gasper) [Ramanujan J. 13 (1-3) (2007), 229-242]
  68. Elliptic determinant evaluations and the Macdonald identities for affine root systems (jointly with Hjalmar Rosengren) [Compos. Math. 142 (4) (2006), 937-961]
  69. Noncommutative extensions of Ramanujan's ₁ψ₁ summation [Electron. Trans. Numer. Anal. 24 (2006), 94-102]
  70. Explicit computation of the q,t-Littlewood-Richardson coefficients [Proceedings of the Workshop on Jack, Hall-Littlewood and Macdonald polynomials (V. Kuznetsov and S. Sahi, eds.) Edinburgh, ICMS, Sept. 23-26, 2003; Contemp. Math. 417 (2006), 335-343]
  71. Inversion of the Pieri formula for Macdonald polynomials (jointly with Michel Lassalle) [Adv. Math. 202 (2) (2006), 289-325]
  72. Summation, transformation, and expansion formulas for multibasic theta hypergeometric series (jointly with George Gasper) [Adv. Stud. Contemp. Math. (Kyungshang) 11 (2005), no. 1, 67-84; also in Proceedings of the Workshop Elliptic Integrable Systems (M. Noumi and K. Takasaki, eds.) Kyoto, RIMS, 2004; Rokko Lectures in Mathematics 18 (2005), 1-17]
  73. Another proof of Bailey's ₆ψ₆ summation (jointly with Frédéric Jouhet) [Aequationes Math. 70 (1-2) (2005), 43-50]
  74. On Warnaar's elliptic matrix inversion and Karlsson-Minton-type elliptic hypergeometric series (jointly with Hjalmar Rosengren) [J. Comput. Appl. Math. 178 (2005), 377-391]
  75. Abel-Rothe type generalizations of Jacobi's triple product identity [in Theory and Applications of Special Functions. A Volume Dedicated to Mizan Rahman (M. E. H. Ismail and E. Koelink, eds.), Dev. Math. 13 (2005), 383-400]
  76. q-Analogues of the sums of consecutive integers, squares, cubes, quarts and quints [Electron. J. Combin. 11 (1) (2004), #R71, 12 pp.]
  77. Some curious extensions of the classical beta integral evaluation [in Mathematics and Computer Science, III (M. Drmota, P. Flajolet, D. Gardy, B. Gittenberger, eds.) Vienna, 2004; Trends Math., Birkhäuser, Basel, 2004, pp. 59-68]
  78. An analytic formula for Macdonald polynomials (jointly with Michel Lassalle) [C. R. Math. Acad. Sci. Paris 337 (9) (2003), 569-574]
  79. Summations and transformations for multiple basic and elliptic hypergeometric series by determinant evaluations (jointly with Hjalmar Rosengren) [Indag. Math. (N.S.) 14 (2003), 483-514]
  80. A nonterminating ₈φ₇ summation for the root system C_r [J. Comput. Appl. Math. 160 (2003), 283-296]
  81. Inversion of bilateral basic hypergeometric series [Electron. J. Combin. 10 (2003), #R10, 27 pp.]
  82. A multidimensional generalization of Shukla's ₈ψ₈ summation [Constr. Approx. 19 (2003), 163-178]
  83. Elementary derivations of identities for bilateral basic hypergeometric series [Selecta Math. (N.S.) 9 (2003) 1, 119-159]
  84. A new A_n extension of Ramanujan's ₁ψ₁ summation with applications to multilateral basic hypergeometric series (jointly with Stephen C. Milne) [in Special Functions 2000 (J. Bustoz and S. K. Suslov, eds.), Rocky Mount. J. Math. 32 (2) (2002), 759-792]
  85. A simple proof of Bailey's very-well-poised ₆ψ₆ summation [Proc. Amer. Math. Soc. 130 (2002), 1113-1123]
  86. Multilateral transformations of q-series with quotients of parameters that are nonnegative integral powers of q [in q-Series with Applications to Combinatorics, Number Theory, and Physics (B. C. Berndt and K. Ono, eds.), Amer. Math. Soc., Providence, R. I., Contemp. Math. 291 (2001), 203-227]
  87. A new multidimensional matrix inversion in A_r [in q-Series from a Contemporary Perspective (M. E. H. Ismail and D. Stanton, eds.), Amer. Math. Soc., Providence, R. I., Contemp. Math. 254 (2000), 413-432]
  88. Summation theorems for multidimensional basic hypergeometric series by determinant evaluations [Discrete Math. 210 (2000), 151-169]
  89. Some new applications of matrix inversions in A_r [Ramanujan J. 3 (1999), 405-461]
  90. A new multidimensional matrix inverse with applications to multiple q-series (jointly with Christian Krattenthaler) [(H. W. Gould Anniversary Volume) Discrete Math. 204 (1999), 249-279; selected to be included in Discrete Math., spec. vol. ``Editors' Choice, Edition 1999'']
  91. Multidimensional matrix inversions and multiple basic hypergeometric series associated to root systems [in Special functions and differential equations (K. Srinivasa Rao, R. Jagannathan, G. Vanden Berghe, and J. Van der Jeugt, eds.), Proceedings of a workshop, WSSF '97, Madras, India, January 13-24, 1997; Allied Publ., New Delhi (1998), 25-30]
  92. C_n and D_n very-well-poised ₁₀φ₉ transformations (jointly with Gaurav Bhatnagar) [Constr. Approx. 14 (1998), 531-567]
  93. Multidimensional matrix inversions and A_r and D_r basic hypergeometric series [Ramanujan J. 1 (1997), 243-274]
  94. Multidimensional matrix inversions [Sém. Lothar. Combin. 35 (1995), B35g, 24 pp.]
• Books and special issues edited:
  • Basic Hypergeometric Series Associated with Root Systems and Applications in honor of Stephen C. Milne's 75th birthday (jointly with G. Bhatnagar, Frank Garvan, and Christian Krattenthaler), Special Issue of SIGMA, under completion.
  • The Krattenthaler Festschrift (jointly with V. Strehl and J.-Y. Thibon), Issue 81 of Sém. Lothar. Combin., completed in April 2020.
  • Elliptic Hypergeometric Functions and Their Applications (jointly with S. V. Spiridonov and S. Ole Warnaar), Special Issue of SIGMA, completed in December 2018.
  • Ramanujan Rediscovered (jointly with N. D. Baruah, B. C. Berndt, S. Cooper and T. Huber), Proceedings of a Conference on Elliptic Functions, Partitions, and q-Series in Memory of K. Venkatachaliengar, Bangalore (1-5 June, 2009); Ramanujan Mathematical Society Lecture Notes Series, Vol. 14, 2010 (also published by International Press, Somerville, MA, USA, 2012)

Editorial boards:

• Journal of Mathematical Analysis and Applications (associate editor since July 2011) [login page]
• The Ramanujan Journal (editorial board member since January 2015) [login page; login at Springer Nature]
• Journal of Algebraic Combinatorics (editorial board member since July 2020) [login page]
• Enumerative Combinatorics and Applications (editorial board member since September 2020)
• Contributions to Discrete Mathematics (editorial board member since June 2023)

Postdocs:

• Past:
  • Nian Hong Zhou
  • Neelam Saikia
  • Guo-Shuai Mao
  • Garima Sood
  • Gaurav Bhatnagar
  • Emma Yu Jin
  • Meesue Yoo
  • Alessandro Conflitti

Ph.D. students:

• Past:
  • Josef Küstner [Ph.D. thesis: Elliptic combinatorics of lattice paths, domino tilings and rook placements, University of Vienna, 2022]
  • Christian Stump [Ph.D. thesis: q,t-Fuß-Catalan numbers for finite reflection groups, University of Vienna, 2008]

Selected events:

• FPSAC'24 (36th International Conference on Formal Power Series and Algebraic Combinatorics), Ruhr-Universität Bochum, Germany, July 22-26, 2024
• The Legacy of Ramanujan 2024, Celebrating the 85th birthdays of George Andrews & Bruce Berndt, Penn State University, USA, June 6-9, 2024
• SLC 91 (Séminaire Lotharingien de Combinatoire 91), Salobreña, Spain, March 17-20, 2024
• ICECA 2023 (International Conference on Enumerative Combinatorics and Applications), Virtual, September 4-6, 2023
• Elliptic Integrable Systems, Representation Theory and Hypergeometric Functions (MSJ-SI 2023 Workshop), University of Tokyo, Tokyo, Japan, July 31-August 4, 2023
• 18th Annual International Conference on Srinivasa Ramanujan, Srinivasa Ramanujan Centre (SRC), Kumbakonam, India, December 20-22, 2022
• ICECA 2022 (International Conference on Enumerative Combinatorics and Applications), Virtual, September 6-7, 2022
• FPSAC'22 (34th International Conference on Formal Power Series and Algebraic Combinatorics), Indian Institute of Science, Bangalore, India, July 18-22, 2022
• Algorithmic and Enumerative Combinatorics (AEC 2022) conference, Vienna, Austria, July 4-8, 2022
• OPSFA 2022 (16th International Symposium on Orthogonal Polynomials, Special Functions and Applications), CRM Montreal, Canada, Online, June 13-17, 2022
• FPSAC'21 (33rd International Conference on Formal Power Series and Algebraic Combinatorics), Bar-Ilan University, Ramat-Gan, Israel, July 5-9, 2021
• Lattice Paths, Combinatorics and Interactions hybrid conference, CIRM, Luminy, Marseille, France, June 21-25, 2021
• International Conference on Special Functions & Applications (ICSFA-2020), Babu Banarasi Das University, Lucknow, Online, December 22-23, 2020
• Hypergeometry, Integrability and Lie Theory, Workshop at the Lorentz Center, Leiden, The Netherlands, Online, December 7-11, 2020
• AMS Fall Eastern Virtual Sectional Meeting, October 3-4, 2020
• FPSAC'20 (32nd International Conference on Formal Power Series and Algebraic Combinatorics), Online, July 6-24, 2020
• ÖMG Conference 2019 (Conference of the Austrian Mathematical Society), University of Applied Sciences Vorarlberg, Dornbirn, Austria, September 16-20, 2019
• OPSFA 2019 (15th International Symposium on Orthogonal Polynomials, Special Functions and Applications), RISC Hagenberg, Austria, July 22-26, 2019
• Elliptic integrable systems, special functions and quantum field theory, Nordita, Stockholm, Sweden, June 16-20, 2019
• Analytic and Combinatorial Number Theory: The Legacy of Ramanujan, A conference in honor of Bruce Berndt's 80th birthday, University of Illinois at Urbana-Champaign, IL, USA, June 6-9, 2019
• Topics on Orthogonal Matters Fest, An informal gathering to celebrate Tom Koornwinder's 75th birthday, Radboud University, Nijmegen, Netherlands, December 10-11, 2018
• SLC 81 (81st Séminaire Lotharingien de Combinatoire 2018/KrattenthalerFest), Strobl, September 9-12, 2018
• Combinatory Analysis, A conference in honor of George Andrews' 80th birthday, Penn State University, State College, PA, USA, June 21-24, 2018
• International Conference on Special Functions, Theory, Computation, and Applications, In Celebration of the 20th Anniversary of the Lie Bie Ju Centre for Mathematical Sciences, City University of Hong Kong, June 5-9, 2017
• Elliptic Hypergeometric Functions in Combinatorics, Integrable Systems and Physics, ESI, Vienna, March 20-24, 2017
• Number Theory in honor of Krishna Alladi's 60th birthday, University of Florida, Gainesville, FL, USA, March 17-21, 2016

Talks:

• Here is an online talk I gave on November 22, 2023, in the Journal of Algebraic Combinatorics Webinar Series:

Curiosities:

• I used to play a lot of chess; for a few (not so recent) games I played, see here, here, and there.