Shaoshi Chen陈绍示

• Symbolic Computation (Symbolic Integration and Summation)
• Differential and Difference Algebra (Galois Theory)
• Combinatorics (Wilf-Zeilberger Method)
• Arithmetic Dynamics (Dynamics of P-Recursive Sequences)

1. Under review
   Cycle structures and parities of linearized permutation polynomials, 2026.
   with Huajun Bian and Dabin Zheng: [PDF]
2. Under review
   On the vanishing coefficients of algebraic power series, 2026.
   with Pietro Corvaja and Umberto Zannier: [PDF]
3. Under review
   On stable patterns and properties on permutations of multisets, 2026.
   with Hanqian Fang and Sergey Kitaev: [PDF]
4. Under review
   Single-exponential Bounds for Diagonals of D-finite Power Series, 2026 .
   with Frederic Chyzak, Pingchuan Ma, and Chaochao Zhu: [PDF]
5. Under review
   Flip Graphs for Polynomial Multiplication, 2025 (updated).
   with Manuel Kauers: [PDF]
6. Accepted · to appear
   Symbolic Integration of Differential Forms: from Abel to Zeilberger, 2026 (updated).
   with David A. Cox and Yisen Wang: [PDF] To appear in Mathematics of Computation.
7. Accepted · to appear
   Telescoping Algorithms for Sigma*-Extensions via Complete Reductions, 2025.
   with Yiman Gao, Hui Huang, and Carsten Schneider: [PDF] To appear in the Proceedings of Recent Trends in Computer Algebra, Springer.
8. Accepted · to appear
   Creative Telescoping, 2025.
   with Manuel Kauers and Christoph Koutschan: [PDF] These notes on creative telescoping is based on a series of lectures at the Institut Henri Poincare in November and December of 2023. To appear in the Proceedings of Recent Trends in Computer Algebra, Springer.
9. Complete Reduction for Derivatives in a Transcendental Liouvillian Extension.
   Journal of Symbolic Computation, Volume 140, 2027, Paper No. 102634.
   with Hao Du, Yiman Gao, Hui Huang, Wenqiao Li, and Ziming Li:
   [Preprint] [Published version] [Bibtex].
   
10. On the Summability Problem of Multivariate Rational Functions in the Mixed Case, 2026.
    Proceedings of ISSAC'26, pp. 96–104, ACM Press, 2026.
    with Lixin Du, Hanqian Fang and Yisen Wang: This paper is dedicated to Professor George Labahn on the occasion of his 75th birthday.
    [Preprint] [Published version] [Bibtex].
    
11. A zero-test for D-algebraic transseries.
    Proceedings of ISSAC'26, pp. 105–113, ACM Press, 2026.
    with Hanqian Fang and Joris van der Hoeven:
    [Preprint] [Published version] [Bibtex].
    
12. Symbolic Integration in Weierstrass-like Extensions, 2026.
    Proceedings of ISSAC'26, pp. 114–123, ACM Press, 2026.
    with Manuel Kauers, Wenqiao Li, Xiuyun Li, and David Masser:
    [Preprint] [Published version] [Bibtex].
    
13. Symbolic Summation of Multivariate Rational Functions.
    Foundations of Computational Mathematics, Volume 26, pp. 1635-1697, 2026.
    with Lixin Du and Hanqian Fang:
    [Preprint] [Published version] [Bibtex]. [Maple package]
    
14. Non-minimality of Minimal Telescopers Explained by Residues.
    Proceedings of ISSAC'25, pp. 70–78, ACM Press, 2025.
    with Manuel Kauers, Christoph Koutschan, Xiuyun Li, Rong-hua Wang and Yisen Wang:
    [Preprint] [Published version] [Bibtex].
    
15. A Unified Reduction for Hypergeometric and q-Hypergeometirc Creative Telescoping.
    The Ramanujan Journal, Volume 68, July 2025, Paper No. 14.
    with Hao Du, Yiman Gao, Hui Huang, and Ziming Li:
    [Preprint] [Published version] [Bibtex].
    Dedicated to Professors George Andrews and Bruce Berndt for their 85th birthdays
    
16. Patterns in Multi-dimensional Permutations.
    European Journal of Combinatorics, Volume 130, December 2025, Paper No. 104203.
    with Hanqian Fang, Sergey Kitaev, and Candice X.T. Zhang:
    [Preprint] [Published version] [Bibtex].
    
17. How to Generate All Possible Rational Wilf-Zeilberger Forms?.
    Journal of Symbolic Computation, Volume 132, 2026, Paper No. 102473.
    with Christoph Koutschan and Yisen Wang:
    [Preprint] [Published version] [Bibtex]. [Supplementary material].
    
18. Reducing hyperexponential functions over monomial extensions.
    Journal of Systems Science and Complexity, 38(3): 1206--1225, 2025.
    with Hao Du, Yiman Gao, and Ziming Li:
    [Preprint] [Published version] [Bibtex].
    
19. Bijections around Springer numbers.
    Discrete Mathematics, Volume 348, Issue 11, November 2025, Paper No. 114570
    with Yang Li, Zhicong Lin, and Sherry H.F. Yan:
    [Preprint] [Published version] [Bibtex].
    
20. Parallel Summation in P-recursive Extensions.
    Proceedings of ISSAC'24, pp. 82–90, ACM Press, 2024.
    with Ruyong Feng, Manuel Kauers, and Xiuyun Li:
    [Preprint] [Published version] [Bibtex].
    
21. Reduction-based Creative Telescoping for P-recursive Sequences via Integral Bases .
    Journal of Symbolic Computation, Volume 126, January--February 2025, 102341
    with Lixin Du, Manuel Kauers, and Rong-Hua Wang:
    [Preprint] [Published version] [Bibtex].
    
22. D-finiteness, rationality, and height III: multivariate Polya-Carlson dichotomy, 2024.
    Mathematische Zeitschrift, Volume 306, article number 70, 2024.
    with Jason P. Bell, Khoa D. Nguyen, and Umberto Zannier:
    [Preprint] [Published version] [Bibtex].
    
23. Telescopers for Differential Forms with One Parameter, 2024.
    Selecta Mathematica New Series, Volume 30, article number 36, 2024.
    with Ruyong Feng, Ziming Li, Michael F. Singer, and Stephen M. Watt:
    [Preprint] [Published version] [Bibtex].
    
24. Hermite Reduction for D-finite Functions via Integral Bases, 2023.
    Proceedings of ISSAC'23, pp. 155–163, ACM Press, 2023.
    with Lixin Du and Manuel Kauers:
    [Preprint] [Published version] [Bibtex].
    
25. Stability Problems on D-finite Functions, 2023.
    Proceedings of ISSAC'23, pp. 164–172, ACM Press, 2023.
    with Ruyong Feng, Zewang Guo and Wei Lu:
    [Preprint] [Published version] [Bibtex].
    
26. Stability Problems in Symbolic Integration, 2022.
    Proceedings of ISSAC'22, pp. 517–524, ACM Press, 2022.
    [Preprint] [Published version] [Bibtex].
    
27. Constructing Minimal Telescopers for Rational Functions in Three Discrete Variables, 2022.
    Advances in Applied Mathematics, 141: 12389, October 2022.
    with Qing-hu Hou, Hui Huang, George Labahn, and Rong-hua Wang:
    [Preprint] [Published version] [Bibtex].
    This paper is dedicated to Professor Ziming Li on the occasion of his 60th birthday
    
28. Rational Dynamical Systems, S-units, and D-finite Power Series, 2021.
    Algebra and Number Theory, 15(7): 1699–1728, 2021.
    with Jason P. Bell and Ehsaan Hossain:
    [Preprint] [Published version] [Bibtex].
    
29. Lazy Hermite Reduction and Creative Telescoping for Algebraic Functions, 2021.
    Proceedings of ISSAC'21, pp. 75–82, ACM Press, 2021.
    with Lixin Du and Manuel Kauers:
    [Preprint] [Published version] [Bibtex].
    
30. Separability Problems in Creative Telescoping, 2021.
    Proceedings of ISSAC'21, pp. 83–90, ACM Press, 2021.
    with Ruyong Feng, Pingchuan Ma and Michael F. Singer:
    [Preprint] [Published version] [Bibtex].
    This paper received the "ISSAC2021 Distinguished Paper Award"
31. On the Existence of Telescopers for Rational Functions in Three Variables, 2020.
    Journal of Symbolic Computation, 104: 494–522, 2021.
    with Lixin Du, Rong-hua Wang and Chaochao Zhu:
    [Preprint] [Published version] [Bibtex].
    
32. Integral Bases for P-Recursive Sequences, 2020.
    Proceedings of ISSAC'20, pp. 91–98, ACM Press, 2020.
    with Lixin Du, Manuel Kauers, and Thibaut Verron:
    [Preprint] [Published version] [Bibtex].
    
33. Existence Problem of Telescopers for Rational Functions in Three Variables: the Mixed Cases.
    Proceedings of ISSAC'19, pp. 82–89, ACM Press, 2019.
    with Lixin Du and Chaochao Zhu:
    [Preprint] [Published version] [Bibtex].
    
34. Apparent Singularities of D-finite Systems.
    Journal of Symbolic Computation, 95: 217–237, 2019.
    with Manuel Kauers,Ziming Li, Yi Zhang :
    [Preprint] [Published version] [Bibtex].
    
35. Proof of the Wilf-Zeilberger Conjecture for Mixed Hypergeometric Terms.
    Journal of Symbolic Computation, 93: 133–147, 2019.
    with Christoph Koutschan:
    [Preprint] [Published version] [Bibtex].
    
36. How to Generate All Possible Rational Wilf-Zeilberger Pairs?.
    Algorithms and Complexity in Mathematics, Epistemology, and Science, edited by N. Fillion, R. M. Corless and I. S. Kotsireas, Fields Institute Communications book series, 82: 17–34, 2019, Springer New York.
    Dedicated to the memory of Jonathan M. Borwein and Ann Johnson:
    [Preprint] [Published version] [Bibtex].
    
37. Additive Decompositions in Primitive Extensions.
    Proceedings of ISSAC'18, pp. 135–142, ACM Press, 2018.
    with Hao Du and Ziming Li:
    [Preprint] [Published version] [Bibtex].
    
38. Bivariate Extensions of Abramov's Algorithm for Rational Summation.
    Advances in Computer Algebra, In Honour of Sergei Abramov's 70th Birthday, edited by C.Schneider, E.Zima, Springer Proceedings in Mathematics and Statistics 226, 93–104, 2018:
    [Preprint] [Published version] [Bibtex].
    
39. Reduction-based Creative Telescoping for Fuchsian D-finite Functions.
    Journal of Symbolic Computation, 85: 108–127, 2018.
    with Mark van Hoeij , Manuel Kauers, Christoph Koutschan:
    [Preprint] [Published version] [Bibtex].
    
40. Power Series with Coefficients from a Finite Set.
    Journal of Combinatorial Theory, Series A., 151: pp. 241–253, 2017.
    with Jason P. Bell:
    [Preprint] [Published version] [Bibtex].
    
41. Some Open Problems Related to Creative Telescoping.
    Journal of Systems Science and Complexity 30(1): pp. 154–172, 2017.
    with Manuel Kauers:
    [Preprint] [Published version] [Bibtex].
    
42. Combinatorics of Hybrid Sets.
    Proceedings of the 18th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC'16), pp. 60–64, IEEE, 2016.
    with Stephen M. Watt:
    [Preprint] [Published version] [Bibtex].
    
43. Existence Problem of Telescopers: Beyond the Bivariate Case.
    Proceedings of ISSAC'16, pp. 167–174, ACM Press, 2016.
    with Qing-hu Hou , George Labahn, Ronghua Wang:
    [Preprint] [Published version] [Bibtex].
    
44. Reduction-Based Creative Telescoping for Algebraic Functions.
    Proceedings of ISSAC'16, pp. 175–182, ACM Press, 2016.
    with Manuel Kauers, Christoph Koutschan:
    [Preprint] [Published version] [Bibtex].
    
45. Desingularization of Ore Operators.
    Journal of Symbolic Computation 74(C): 617-626, 2016.
    with Manuel Kauers, Michael F. Singer :
    [Preprint] [Published version] [Bibtex].
    
46. A Modified Abramov-Petkovsek Reduction and Creative Telescoping for Hypergeometric Terms.
    Proceedings of ISSAC'15, pp. 117–124, ACM Press, 2015.
    with Hui Huang, Manuel Kauers, Ziming Li :
    [Preprint] [Published version] [Bibtex].
    
47. On the Existence of Telescopers for Mixed Hypergeometric Terms
    Journal of Symbolic Computation 68:1-26, 2015.
    with Frédéric Chyzak, Ruyong Feng, Guofeng Fu, Ziming Li:
    [Preprint] [Published version] [Bibtex].
    
48. Parallel Telescoping and Parameterized Picard-Vessiot Theory.
    Proceedings of ISSAC'14, pp. 99–106, ACM Press, 2014.
    with Ruyong Feng, Ziming Li, Michael F. Singer:
    [Preprint] [Published version] [Bibtex].
    
49. A Generalized Apagodu-Zeilberger Algorithm.
    Proceedings of ISSAC'14, pp. 107–114, ACM Press, 2014.
    with Manuel Kauers, Christoph Koutschan:
    [Preprint] [Published version] [Bibtex].
    
50. On the Summability of Bivariate Rational Functions.
    Journal of Algebra, 409(2):320–343, 2014.
    with Michael F. Singer :
    [Preprint] [Published version] [Bibtex].
    
51. Hermite Reduction and Creative Telescoping for Hyperexponential Functions.
    Proceedings of ISSAC'13, pp. 77–84, ACM Press, 2013.
    with Alin Bostan, Frédéric Chyzak, Ziming Li, Guoce Xin : [Supplementary material].
    [Preprint] [Published version] [Bibtex].
    
52. Desingularization Explains Order-Degree Curves for Ore Operators.
    Proceedings of ISSAC'13, pp. 157–164, ACM Press, 2013.
    with Maximilian Jaroschek, Manuel Kauers, Michael F. Singer:
    [Preprint] [Published version] [Bibtex].
    
53. A Note on the Diagonal Theorem of Bivariate Rational Formal Power Series (in Chinese).
    Acta Mathematica Sinica Chinese Series, 56 (2): 203--210, 2013.
    with Xiaoli Wu:
    [Preprint] [Published version] [Bibtex].
    
54. Multiplicative Decompositions of Multivariate q-Hypergeometric Terms (in Chinese).
    Journal of System Science and Mathematical Science Chinese Series, 32 (8): 1019-1032, 2012.
    with Ruyong Feng, Guofeng Fu, Jin Kang:
    [Preprint] [Published version] [Bibtex].
    
55. Residues and Telescopers for Bivariate Rational Functions.
    Advance in Applied Mathematics, 49(2):111–133, 2012.
    with Michael F. Singer :
    [Preprint] [Published version] [Bibtex].
    
56. Order-Degree Curves for Hypergeometric Creative Telescoping.
    Proceedings of ISSAC'12, pp. 122–129, ACM Press, 2012.
    with Manuel Kauers:
    [Preprint] [Published version] [Bibtex].
    
57. Telescopers for Rational and Algebraic Functions via Residues.
    Proceedings of ISSAC'12, pp. 130–137, ACM Press, 2012.
    with Manuel Kauers, Michael F. Singer :
    [Preprint] [Published version] [Bibtex].
    
58. Trading Order for Degree in Creative Telescoping
    Journal of Symbolic Computation 47(8):968-995, 2012.
    with Manuel Kauers:
    [Preprint] [Published version] [Bibtex].
    
59. On the Structure of Compatible Rational Functions.
    Proceedings of ISSAC'11, pp. 91–98, ACM Press, 2011.
    with Ruyong Feng, Guofeng Fu, Ziming Li :
    [Preprint] [Published version] [Bibtex].
    
60. Complexity of Creative Telescoping for Bivariate Rational Functions.
    Proceedings of ISSAC'10, pp. 203–210, ACM Press, 2010.
    with Alin Bostan, Frédéric Chyzak, Ziming Li :
    [Preprint] [Published version] [Bibtex] [Maple Codes]
    

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Appointments

• 2024/04 -- present, Full Professor, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, China.
• 2017/03 -- 2024/04, Associate Professor, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, China.
• 2013/07 -- 2017/03, Assistant Professor, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, China.
• 2015/10 -- 2016/08, Fields-Ontario Postdoctoral Fellow, Fields Institute and Faculty of Mathematics, University of Waterloo, Ontario, Canada

  Working with Stephen M. Watt and George Labahn.

• 2011/08 -- 2013/07, Post-Doctoral Fellow, Department of Mathematics, North Carolina State University, Raleigh, USA.

  Working with Michael F. Singer.

• 2011/02 -- 2011/08, Post-Doctoral Fellow, Research Institute for Symbolic Computation, Johannes Kepler University Linz, Hagenberg, Austria.

  Working with Manuel Kauers.

Professional service & editorial boards

Academic Positions

Editorial Boards

1. Rational-Transcendental Dichotomy Theorems on Power Series with Arithmetic Restrictions. Number Theory Web Seminar, February 27, 2025. [Slides]
2. Separability Problems in Creative Telescoping. ISSAC2021, Saint Petersburg, Russia, July 20, 2021. [Slides] [Paper]
3. A Reduction Approach to Creative Telescoping. ISSAC2019 Tutorial Lectures, Beihang University, Beijing, China, 2019. [Slides] [Extended Abstract]
4. How to generate all possible WZ-pairs algorithmically? Chinese Mathematical Society 2018 Annual Conference, Guiyang, Guizhou, China, 2018. [Slides]
5. Symbolic Integration: A Brief Introduction. Seminar at the School of Mathematics, Liaoning Normal University, Dalian, China, 2018. [Slides]
6. D-finite Generating Functions in Enumerative Combinatorics. Chinese Congress on Combinatorics and Graph Theory 2018, Hefei, China, 2018. [Slides]
7. Rationality Theorems on D-finite Power Series. Seminar at the School of Mathematical Sciences, East China Normal University, Shanghai, China, 2018. [Slides]
8. Reduction-based Algorithms for Creative Telescoping. Joint International Meeting of CMS-AMS, Shanghai, China, 2018. [Slides]
9. D-finite Functions: Algorithmic, Analytic and Arithmetic Aspects. Computer Mathematics 2017, Xiangtan, China, 2017. [Slides]
10. Power Series with Coefficients from a Finite Set. Lattice walks at the Interface of Algebra, Analysis and Combinatorics (2017), Banff, Canada, 2017. [Slides]
11. Creative Telescoping: Theory and Algorithms. MITACS Seminar Series/ORCCA Joint Lab Meeting, Western University, Canada, 2016. [Slides]

1. Linear Algebra (2014-2015) at University of Chinese Academy of Sciences.
2. Linear Algebra (2016-2017) at University of Chinese Academy of Sciences.
3. Abstract Algebra II (2019-2020) at Beihang University.
4. Abstract Algebra II (2021-2021) at Beihang University.

Students

1. Yuhao Zhao (赵昱皓，2026/09-2031/07)
2. Guangxin Zheng (郑广欣，2025/09-2030/07)
3. Chen Li (李宸，2024/09-2029/07)
4. Huajun Bian (边华俊，2023/09-2028/07)
5. Hanqian Fang (方涵芊，2022/09-2027/07， joint PhD student with Joris van der Hoeven)
6. Xiuyun Li (李秀云，2021/09-2026/07, joint PhD student with Manuel Kauers)
7. Yisen Wang (王艺森，2021/09-2026/07, joint PhD student with Christoph Koutschan)
8. Pingchuan Ma (马平川，2019/09-2024/07, joint PhD student with Frederic Chyzak，now at Tsinghua University High School)
9. Lixin Du (杜丽欣，2017/09-2022/07, joint PhD student with Manuel Kauers)
10. Chaochao Zhu (朱超超，2016/09-2021/07, now at West Anhui University)

Postdocs

1. Candice X.T. Zhang (张旭彤， 2024/07-2026/08)
2. Yingrui Zhang (张英瑞， 2022/07-2024/08)
3. Tianlong Yu (虞天龙， 2021/07-2024/05)

• 2001/09 -- 2005/07, B.Sci., Mathematics, Jiangsu University , Jiangsu, China.
• 2005/09 -- 2010/12, Ph.D., Applied Mathematics, Academy of Mathematics and Systems Science , Chinese Academy of Sciences, Beijing, China.

Supervisor:  Ziming Li (AMSS, China).

• 2007/12 -- 2011/02, Ph.D., Computer Science, co-directed between Academy of Mathematics and Systems Science (Beijing, China) and École Polytechnique (Paris, France).

Co-supervisors:  Frédéric Chyzak (INRIA, France) and Ziming Li (AMSS, China).

Dissertation: Some Applications of Differential-Difference Algebra to Creative Telescoping (version in Chinese)

Research notes · unpublished

1. A Note on Lipshitz's Lemma 3.
   with Ziming Li, 2011: [PDF].
2. A Note on Ostrogradsky and Horowitz's Method.
   with Ziming Li, 2010: [PDF].
3. A Exercise on Real Elementary Functions in the Book "Symbolic Integration I" (second edition) .
   with Ruyong Feng, Ziming Li, Huaifu Wang, 2008: [PDF].

Seminars & conferences

1. Workshop on the Frontiers in Arithmetic Dynamics (FIAD2024)
2. ACA 2022 Special Session: D-finite Functions and Beyond: Algorithms, Combinatorics, and Arithmetic