辻本 諭 教授

京都大学大学院情報学研究科
数理工学コース
〒606-8501 京都市左京区吉田本町

e-mail: tsujimoto.satoshi.5s _at_ kyoto-u.jp

オフィス：総合研究10号館3階316号室

講義について

学部講義
  • 「線形代数学A・B」
  • 「応用代数学」
大学院講義
  • 「数理解析特論」
  • 「システム解析通論」

研究活動

研究会・学会
  • 18th Orthogonal Polynomials, Special Functions and Applications (OPSFA 18), 2026年8月17日〜21日, 同志社大学
    OPSFA18 HP
  • 日本応用数理学会 2024年度 年会, 2024年9月14日〜16日, 京都大学
    年会 HP
  • Discrete integrable systems: difference equations, cluster algebras and probabilistic models, ICTS, Bengaluru, India
    Program HP
研究テーマ
  • 直交多項式の理論と応用
  • 可積分系の数理
    • ソリトン（粒子性を有する孤立波）
    • 連続・離散・超離散
    • 箱玉系 (ソリトン・オートマトン)
著書
最近の論文（投稿中を含む）
  • Nicolas Crampe, Julien Gaboriaud, Satoshi Tsujimoto: Change of basis for the tridiagonal pairs of type II [arXiv]
  • Nicolas Crampe, Satoshi Tsujimoto, Luc Vinet, Alexei Zhedanov: Algebras behind the bispectrality of the Wilson rational functions and their 4φ3 limits [arXiv]
  • Atsushi Maeno, Satoshi Tsujimoto, Fumitaka Yura: Solitons in 3-State Mealy Automata [arXiv]
  • Pierre-Antoine Bernard, Abderahmane Bouziane, Samuel Pellerin, Simone Têtu, Satoshi Tsujimoto, Luc Vinet, Meri Zaimi, Alexei Zhedanov: Meta algebras and biorthogonal rational functions: the q-Hahn case [arXiv]
  • Satoshi Tsujimoto, Luc Vinet, Alexei Zhedanov : Meta Algebras and Biorthogonal Rational Functions: The Hahn Case [arXiv]
  • Ryoto Watanabe, Masashi Iwasaki, Satoshi Tsujimoto: Discretization of Camassa-Holm peakon equation using orthogonal polynomials and matrix LR transformations [arXiv]
  • Yu Luo, Satoshi Tsujimoto and Hao Yang: Recurrence relations of exceptional Laurent biorthogonal polynomials, Constructive Approximation, DOI:10.1007/s00365-024-09698-w, [arXiv]
  • Astushi Maeno and Satoshi Tsujimoto: Arc lines for the box-ball system related to the ultradiscrete relativistic Toda equation, JSIAM Letters 16 (October 2024), pp.93-96, DOI:10.14495/jsiaml.16.93
  • Satoshi Tsujimoto, Luc Vinet and Alexei Zhedanov: Meta Algebras and Biorthogonal Rational Functions: The Hahn Case [arXiv]
  • Katsuki Kobayashi and Satoshi Tsujimoto: Generalization of the ε-BBS and the Schensted insertion algorithm, to appear in Journal of Algebraic Combinatorics. [arXiv]
  • Satoshi Tsujimoto, Tsuyoshi Kato, Ryosuke Kojima, Kazuki Maeda and Francesco Zanlungo: Analysis of Autonomous Many-Body Particle Models from Geometric Perspective and Its Applications, in: Advanced Mathematical Science for Mobility Society, eds. K. Ikeda, Y. Kawamura, K. Makino, S. Tsujimoto, N. Yamashita, S. Yoshizawa and H. Sumita, Springer Singapore, pp.11-34 (2024), DOI:10.1007/978-981-99-9772-5
  • Yu Luo and Satoshi Tsujimoto: Exceptional Laurent biorthogonal polynomials through spectral transformations of generalized eigenvalue problems, Studies in Applied Mathematics (2023), pp.1-31, DOI: 10.1111/sapm.12603 [arXiv]
  • Katsuki Kobayashi, Kazuki Maeda and Satoshi Tsujimoto: An isospectral transformation between Hessenberg matrix and Hessenberg–bidiagonal matrix pencil without using subtraction. [arXiv]
  • Hiroshi Miki, Satoshi Tsujimoto and Da Zhao: Quantum walk on extension of association schemes, to appear in Journal of Physics A: Mathematical and Theoretical. [arXiv]
  • Hiroshi Miki, Satoshi Tsujimoto and Luc Vinet: The single-indexed exceptional Krawtchouk polynomials, Journal of Difference Equations and Applications, 29:3 (2023) pp. 344-365, DOI: 10.1080/10236198.2023.2202283, [arXiv]
過去の論文（2010から）
  • Atsushi Maeno and Satoshi Tsujimoto: Linearization of the box-ball system with box capacity L, Journal of the Physical Society of Japan, 92 (2023), 024003 (10 pages). [doi][arXiv]
  • David A. Croydon, Makiko Sasada and Satoshi Tsujimoto: General solutions for KdV- and Toda-type discrete integrable systems based on path encodings, Mathematical Physics, Analysis and Geometry, 25 (2022), 27 (71 pages). [doi][arXiv]
  • Hiroshi Miki, Satoshi Tsujimoto, Luc Vinet: Classical and quantum walks on paths associated with exceptional Krawtchouk polynomials, Journal of Mathematical Physics 63 (October 2022), 103502. [doi][arXiv]
  • Hiroshi Miki, Satoshi Tsujimoto and Luc Vinet: Perfect state transfer in two dimensions and the bivariate dual-Hahn polynomials, Progress of Theoretical and Experimental Physics 2022 (April 2022), 053A01(14pp). [doi][arXiv]
  • David Croydon, Tsuyoshi Kato, Makiko Sasada and Satoshi Tsujimoto: Dynamics of the box-ball system with random initial conditions via Pitman's transformation, Memoirs of the American Mathematical Society 283 (March 2023), 1389 (99pp). [doi][arXiv]
  • Katsuki Kobayashi and Satoshi Tsujimoto: The ultradiscrete Toda lattice computes the Smith normal form of bidiagonal matrices, Journal of Mathematical Physics 62 (September 2021), 092701 (8pp). [doi][arXiv]
  • Xiang-Ke Chang, Shi-Hao Li, Satoshi Tsujimoto and Guo-Fu Yu: Two-parameter generalisations of Cauchy bi-orthogonal polynomials and integrable lattices, Journal of Nonlinear Science 31 (March 2021), 30 (23pp). [doi][arXiv]
  • Satoshi Tsujimoto, Luc Vinet and Alexei Zhedanov: The rational Heun operator and Wilson biorthogonal functions, The Ramanujan Journal, (May 2021), https://doi.org/10.1007/s11139-020-00383-7 (23pp). [doi][arXiv]
  • Satoshi Tsujimoto, Luc Vinet and Alexei Zhedanov: An algebraic description of the bispectrality of the biorthogonal rational functions of Hahn type, Proceedings of the American Mathematical Society, 149 (November 2020), pp.715-728. [doi][arXiv]
  • Julien Gaboriaud, Satoshi Tsujimoto, Luc Vinet and Alexei Zhedanov: Degenerate Sklyanin algebras, Askey–Wilson polynomials and Heun operators, Journal of Physics A: Mathematical and Theoretical 53 (October 2020), 445204 (19pp). [doi][arXiv]
  • Geoffroy Bergeron, Nicolas Crampé, Satoshi Tsujimoto, Luc Vinet, and Alexei Zhedanov: The Heun–Racah and Heun–Bannai–Ito algebras, Journal of Mathematical Physics 61 (August 2020), 081701 (15pp). [doi][arXiv]
  • David Croydon, Makiko Sasada and Satoshi Tsujimoto: Dynamics of the ultra-discrete Toda lattice via Pitman’s transformation, RIMS Kokyuroku Bessatsu B78 (2020 April), pp.233-248. [arXiv]
  • Hiroshi Miki, Satoshi Tsujimoto and Luc Vinet: Spin Chains, Graphs and State Revival, In: Foupouagnigni M., Koepf W. (eds) Orthogonal Polynomials. AIMSVSW 2018. Tutorials, Schools, and Workshops in the Mathematical Sciences. Birkhäuser, Cham (March 2020), pp.495-516. [doi][arXiv]
  • Yu Luo, Satoshi Tsujimoto, Luc Vinet and Alexei Zhedanov: Dunkl-Supersymmetric orthogonal functions associated with classical orthogonal polynomials, Journal of Physics A: Mathematical and Theoretical 53 (January 2020), 085205 (16pp). [doi][arXiv]
  • Pascal Baseilhac, Satoshi Tsujimoto, Luc Vinet and Alexei Zhedanov: The Heun-Askey-Wilson algebra and the Heun operator of Askey-Wilson type, Annales Henri Poincaré 20, pp.3091-3112 (2019). [doi][arXiv]
  • Hiroshi Miki, Satoshi Tsujimoto and Luc Vinet: Quantum walks on graphs of the ordered Hamming scheme and spin networks, SciPost Physics 7, 001 (2019). [doi][arXiv]
  • Satoshi Tsujimoto, Luc Vinet and Alexei Zhedanov: Double affine Hecke algebra of rank 1 and orthogonal polynomials on the unit circle, Constructive Approximation 50, pp.209-241 (2019). [doi][arXiv]
  • Yu Luo and Satoshi Tsujimoto: Exceptional Bannai-Ito polynomials, Journal of Approximation Theory 239, pp.144-173 (2019). [doi][arXiv]
  • Geoffroy Bergeron, Luc Vinet and Satoshi Tsujimoto: Generating functions for the Bannai-Ito polynomials, Proceedings of the American Mathematical Society 146, pp.5077-5090 (2018). [doi][arXiv]
  • Saburo Kakei, Jonathan J.C. Nimmo, Satoshi Tsujimoto and Ralph Willox: Linearization of the box-ball system: an elementary approach, Journal of Integrable Systems 3, pp.1-32 (2018). [doi] [arXiv]
  • Satoshi Tsujimoto, Luc Vinet, Guo-Fu Yu and Alexei Zhedanov: Symmetric abstract hypergeometric polynomials, Journal of Mathematical Analysis and Applications 458, pp.742-754 (2018). [doi] [arXiv]
  • Satoshi Tsujimoto, Luc Vinet and Alexei Zhedanov: Tridiagonal representations of the q-oscillator algebra and Askey-Wilson polynomials, Journal of Physics A: Mathematical and Theoretical 50, 235292(15pp) (2017). [doi] [arXiv]
  • Vincent X. Genest, Satoshi Tsujimoto, Luc Vinet and Alexei Zhedanov: Persymmetric Jacobi matrices, isospectral deformations and orthogonal polynomials, Journal of Mathematical Analysis and Applications 450, pp.915-928 (2017). [arXiv]
  • Tsuyoshi Kato, Satoshi Tsujimoto and Andrzej Zuk: Spectral analysis of transition operators, Automata groups and translation in BBS, Communications in Mathematical Physics 350, pp.205-229 (2017). [arXiv]
  • Kazuki Maeda and Satoshi Tsujimoto: A generalized eigenvalue algorithm for tridiagonal matrix pencils based on a nonautonomous discrete integrable system, Journal of Computational and Applied Mathematics 300, pp.134-154 (2016).
  • Hendrik De Bie, Vincent X. Genest, Satoshi Tsujimoto, Luc Vinet and Alexei Zhedanov: The Bannai-Ito algebra and some applications, Journal of Physics: Conference Series 597, conference 1, 12001 (2015).
  • Hiroshi Miki and Satoshi Tsujimoto: A new recurrence formula for generic exceptional orthogonal polynomials, Journal of Mathematical Physics 56, 033502 (2015).
  • Maxim Derevyagin, Satoshi Tsujimoto and Luc Vinet, Alexei Zhedanov: Bannai-Ito polynomials and dressing chains, Proceedings of the American Mathematical Society 142, pp.4191-4206 (2014).
  • Satoshi Tsujimoto, Tsuyoshi Kato and Andrzej Zuk: Automata groups and box-ball systems (オートマタ群と箱玉系), RIMS Kôkyûroku Bessatsu B47, pp.163-170 (2014).
  • Kazuki Maeda and Satoshi Tsujimoto: Direct connection between the RII chain and the nonautonomous discrete modified KdV lattice, Symmetry, Integrability and Geometry: Methods and Applications 9, 073 (2013).
  • 前田一貴, 三木啓司, 辻本 諭: 直交多項式理論からみえてくる可積分系, 日本応用数理学会論文誌 23, pp.341-380 (2013).
  • Satoshi Tsujimoto: Construction of the exceptional orthogonal polynomials and its application to the superintegrable system, in: The breadth and depth of nonlinear discrete integrable systems, ed. T. Tokihiro, RIMS Kôkyûroku Bessatsu B41, pp.181-205 (2013).
  • Yi He, Xing-Biao Hu, Hon-Wah Tam and Satoshi Tsujimoto: Convergence acceleration algorithms related to a generalized E-transformation and its particular cases, Japan Journal of Industrial and Applied Mathematics 30, pp.263-285 (2013).
  • Masatoshi Noumi, Satoshi Tsujimoto and Yasuhiko Yamada: Padé interpolation for elliptic Painlevé equation, in: Symmetries, Integrable Systems and Representations, eds. K. Iohara et al., Springer Proceedings in Mathematics & Statistics 40, pp 463-482 (2013). [arXiv]
  • Tsuyoshi Kato and Satoshi Tsujimoto: A rough analytic relation on partial differential equations, Journal of Mathematics Research 4, pp 125-139 (2012). [arXiv]
  • Hiroshi Miki, Satoshi Tsujimoto, Luc Vinet and Alexei Zhedanov: An algebraic model for the multiple Meixner polynomials of the first kind, Journal of Physics A: Mathematical and Theoretical 45, 325205 (2012). [arXiv]
  • Hiroshi Miki, Satoshi Tsujimoto, Luc Vinet and Alexei Zhedanov: Quantum state transfer in a two-dimensional regular spin lattice of triangular shape, Physical Review A 85, 062306 (2012). [arXiv]
  • Satoshi Tsujimoto, Luc Vinet and Alexei Zhedanov: Dual -1 Hahn polynomials: "Classical'' polynomials beyond the Leonard duality, Proceedings of the American Mathematical Society 141, pp.959-970 (2013). [arXiv]
  • Satoshi Tsujimoto, Luc Vinet and Alexei Zhedanov: Dunkl shift operators and Bannai-Ito polynomials, Advances in Mathematics, Vol.229, pp.2123-2158 (March 2012). [arXiv]
  • Hiroshi Miki, Hiroaki Goda and Satoshi Tsujimoto: Discrete spectral transformations of skew orthogonal polynomials and associated discrete integrable systems, SIGMA, Vol.8, 008, 14 pages (February 2012). [arXiv]
  • Satoshi Tsujimoto, Luc Vinet and Alexei Zhedanov: Jordan algebras and orthogonal polynomials, Journal of Mathematical Physics, Vol.52, 103512, 8 pages (October 2011). [arXiv]
  • Satoshi Tsujimoto, Luc Vinet and Alexei Zhedanov: From slq(2) to a parabosonic Hopf algebra, SIGMA, Vol.7, 093, 13 pages (October 2011). [arXiv]
  • Ryu Sasaki, Satoshi Tsujimoto and Alexei Zhedanov: Exceptional Laguerre and Jacobi polynomials and the corresponding potentials through Darboux-Crum transformations, Journal of Physics A: Mathematical and Theoretical, Vol.43, 315204, 20 pages (August 2010). [arXiv]
  • Kazuki Maeda and Satoshi Tsujimoto: Box-ball systems related to the nonautonomous ultradiscrete Toda equation on the finite lattice, JSIAM Letters, Vol.2, pp. 95-98 (October 2010).
過去の研究会
  • Box-ball systems from integrable systems and probabilistic perspectives, September 19-23, 2022, Montreal, Canada
    Workshop HP : Centre de Recherches Mathématiques (CRM)
  • 13TH International Conference on Symmetries and Integrablity of Difference Equations
    SIDE13 Conference HP
  • 平成２９年度九州大学応力研共同利用研究集会「非線形波動研究の新潮流 ー理論とその応用ー」
    研究集会HP
  • 平成２８年度九州大学応力研共同利用研究集会「非線形波動研究の深化と展開」
    研究集会HP
研究助成
  • 科研費基盤研究(B)
学位
博士(工学)(早稲田大学)
所属学会
日本数学会，日本応用数理学会, 日本物理学会

教育活動

担当授業科目 (大学院)
数理解析特論，システム解析通論
担当授業科目 (学部)
線形代数学A・B，応用代数学

リンク