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You searched for subject:(Box Ball System). Showing records 1 – 3 of 3 total matches.

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University of Arizona

1. Ramalheira-Tsu, Jonathan. The Kostant-Toda Lattice, Combinatorial Algorithms and Ultradiscrete Dynamics .

Degree: 2020, University of Arizona

We study the relationship between the algorithm underlying the Robinson-Schensted-Knuth correspondence (Schensted insertion) and the Toda lattice, exploring this in the settings of discrete-time, ultradiscrete, and continuous-time dynamical systems. Starting with the work of Noumi and Yamada and their observation of a similarity between Hirota's discrete-time Toda lattice and Kirillov's geometric lifting of the RSK (geometric RSK) equations for Schensted insertion, we derive solutions to the former in its unbounded setting and provide an explicit embedding of geometric RSK in the discrete-time Toda lattice. Mimicking the ultradiscretisation of the discrete-time Toda lattice to the soliton cellular automaton, the box-ball system, we produce an extension of the classical box-ball system for Schensted insertion, which we call the ghost-box-ball system. We study this new cellular automaton in relation to Schensted insertion, demonstrating their equivalence, both on their respective coordinatisation and also on the algorithmic level. O'Connell et al. demonstrate an impressive treatment of the relation between a continuous version of geometric RSK and the Toda lattice. Through the introduction of dressing transformations and Painleve analysis, we reformulate some of these connections in a more integrable systems theoretic way. In this continuous setting, we also see the general Toda flows arise and present results on the Poisson geometry of the full Kostant-Toda lattice to lay the foundation for future probing of these exciting connections between algorithms, combinatorics and dynamical systems theory. Advisors/Committee Members: Ercolani, Nicholas M (advisor), Lega, Joceline C. (committeemember), Glickenstein, David A. (committeemember), Cherkis, Sergey (committeemember).

Subjects/Keywords: Box-Ball System; Combinatorics; Dynamical Systems; Integrable Systems; Robinson-Schensted-Knuth Correspondence; The Toda Lattice

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Ramalheira-Tsu, J. (2020). The Kostant-Toda Lattice, Combinatorial Algorithms and Ultradiscrete Dynamics . (Doctoral Dissertation). University of Arizona. Retrieved from http://hdl.handle.net/10150/648656

Chicago Manual of Style (16th Edition):

Ramalheira-Tsu, Jonathan. “The Kostant-Toda Lattice, Combinatorial Algorithms and Ultradiscrete Dynamics .” 2020. Doctoral Dissertation, University of Arizona. Accessed May 08, 2021. http://hdl.handle.net/10150/648656.

MLA Handbook (7th Edition):

Ramalheira-Tsu, Jonathan. “The Kostant-Toda Lattice, Combinatorial Algorithms and Ultradiscrete Dynamics .” 2020. Web. 08 May 2021.

Vancouver:

Ramalheira-Tsu J. The Kostant-Toda Lattice, Combinatorial Algorithms and Ultradiscrete Dynamics . [Internet] [Doctoral dissertation]. University of Arizona; 2020. [cited 2021 May 08]. Available from: http://hdl.handle.net/10150/648656.

Council of Science Editors:

Ramalheira-Tsu J. The Kostant-Toda Lattice, Combinatorial Algorithms and Ultradiscrete Dynamics . [Doctoral Dissertation]. University of Arizona; 2020. Available from: http://hdl.handle.net/10150/648656


Kyoto University / 京都大学

2. Maeda, Kazuki. Theory of Discrete and Ultradiscrete Integrable Finite Lattices Associated with Orthogonal Polynomials and Its Applications : 直交多項式に付随する離散・超離散可積分有限格子の理論とその応用.

Degree: 博士(情報学), 2014, Kyoto University / 京都大学

新制・課程博士

甲第18400号

情博第515号

Subjects/Keywords: discrete finite Toda lattice; box-ball system; generalized eigenvalue algorithm; orthogonal polynomials; Miura type transformation

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Maeda, K. (2014). Theory of Discrete and Ultradiscrete Integrable Finite Lattices Associated with Orthogonal Polynomials and Its Applications : 直交多項式に付随する離散・超離散可積分有限格子の理論とその応用. (Thesis). Kyoto University / 京都大学. Retrieved from http://hdl.handle.net/2433/188859 ; http://dx.doi.org/10.14989/doctor.k18400

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Maeda, Kazuki. “Theory of Discrete and Ultradiscrete Integrable Finite Lattices Associated with Orthogonal Polynomials and Its Applications : 直交多項式に付随する離散・超離散可積分有限格子の理論とその応用.” 2014. Thesis, Kyoto University / 京都大学. Accessed May 08, 2021. http://hdl.handle.net/2433/188859 ; http://dx.doi.org/10.14989/doctor.k18400.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Maeda, Kazuki. “Theory of Discrete and Ultradiscrete Integrable Finite Lattices Associated with Orthogonal Polynomials and Its Applications : 直交多項式に付随する離散・超離散可積分有限格子の理論とその応用.” 2014. Web. 08 May 2021.

Vancouver:

Maeda K. Theory of Discrete and Ultradiscrete Integrable Finite Lattices Associated with Orthogonal Polynomials and Its Applications : 直交多項式に付随する離散・超離散可積分有限格子の理論とその応用. [Internet] [Thesis]. Kyoto University / 京都大学; 2014. [cited 2021 May 08]. Available from: http://hdl.handle.net/2433/188859 ; http://dx.doi.org/10.14989/doctor.k18400.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Maeda K. Theory of Discrete and Ultradiscrete Integrable Finite Lattices Associated with Orthogonal Polynomials and Its Applications : 直交多項式に付随する離散・超離散可積分有限格子の理論とその応用. [Thesis]. Kyoto University / 京都大学; 2014. Available from: http://hdl.handle.net/2433/188859 ; http://dx.doi.org/10.14989/doctor.k18400

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation


Kyoto University

3. Maeda, Kazuki. Theory of Discrete and Ultradiscrete Integrable Finite Lattices Associated with Orthogonal Polynomials and Its Applications .

Degree: 2014, Kyoto University

Subjects/Keywords: discrete finite Toda lattice; box-ball system; generalized eigenvalue algorithm; orthogonal polynomials; Miura type transformation

Record DetailsSimilar RecordsGoogle PlusoneFacebookTwitterCiteULikeMendeleyreddit

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Maeda, K. (2014). Theory of Discrete and Ultradiscrete Integrable Finite Lattices Associated with Orthogonal Polynomials and Its Applications . (Thesis). Kyoto University. Retrieved from http://hdl.handle.net/2433/188859

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Maeda, Kazuki. “Theory of Discrete and Ultradiscrete Integrable Finite Lattices Associated with Orthogonal Polynomials and Its Applications .” 2014. Thesis, Kyoto University. Accessed May 08, 2021. http://hdl.handle.net/2433/188859.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Maeda, Kazuki. “Theory of Discrete and Ultradiscrete Integrable Finite Lattices Associated with Orthogonal Polynomials and Its Applications .” 2014. Web. 08 May 2021.

Vancouver:

Maeda K. Theory of Discrete and Ultradiscrete Integrable Finite Lattices Associated with Orthogonal Polynomials and Its Applications . [Internet] [Thesis]. Kyoto University; 2014. [cited 2021 May 08]. Available from: http://hdl.handle.net/2433/188859.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Maeda K. Theory of Discrete and Ultradiscrete Integrable Finite Lattices Associated with Orthogonal Polynomials and Its Applications . [Thesis]. Kyoto University; 2014. Available from: http://hdl.handle.net/2433/188859

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

.