49 citations · 348 across the 45 of their papers we have counts for
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The ultradiscrete Toda lattice and the Smith normal form of bidiagonal matrices
Katsuki Kobayashi, Satoshi Tsujimoto
The discrete Toda lattice preserves the eigenvalues of tridiagonal matrices, and convergence of dependent variables to the eigenvalues can be proved under appropriate conditions. W…
Bi-infinite solutions for KdV- and Toda-type discrete integrable systems based on path encodings
David A. Croydon, Makiko Sasada, Satoshi Tsujimoto
We define bi-infinite versions of four well-studied discrete integrable models, namely the ultra-discrete KdV equation, the discrete KdV equation, the ultra-discrete Toda equation,…
Perfect state transfer in two dimensions and the bivariate dual-Hahn polynomials
Hiroshi Miki, Satoshi Tsujimoto, Luc Vinet
A new solvable two-dimensional spin lattice model defined on a regular grid of triangular shape is proposed. The hopping amplitudes between sites are related to recurrence coeffici…
Two-parameter generalisations of Cauchy bi-orthogonal polynomials and integrable lattices
Xiang-Ke Chang, Shi-Hao Li, Satoshi Tsujimoto +1
In this article, we consider the generalised two-parameter Cauchy two-matrix model and corresponding integrable lattice equation. It is shown that with parameters chosen as …
An algebraic description of the bispectrality of the biorthogonal rational functions of Hahn type
Satoshi Tsujimoto, Luc Vinet, Alexei Zhedanov
The biorthogonal rational functions of the type on the uniform grid provide the simplest example of rational functions with bispectrality properties that are similar to t…
Degenerate Sklyanin algebras, Askey-Wilson polynomials and Heun operators
Julien Gaboriaud, Satoshi Tsujimoto, Luc Vinet +1
The -difference equation, the shift and the contiguity relations of the Askey-Wilson polynomials are cast in the framework of the three and four-dimensional degenerate Sklyanin…