272 citations · 2.2k across the 97 of their papers we have counts for
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Multispecies totally asymmetric zero range process: I. Multiline process and combinatorial
Atsuo Kuniba, Shouya Maruyama, Masato Okado
We introduce an -species totally asymmetric zero range process (-TAZRP) on one-dimensional periodic lattice with sites. It is a continuous time Markov process in which $n…
Multispecies TASEP and the tetrahedron equation
Atsuo Kuniba, Shouya Maruyama, Masato Okado
We introduce a family of layer to layer transfer matrices in a three-dimensional (3D) lattice model which can be viewed as partition functions of the -oscillator valued six-vert…
Combinatorial Yang-Baxter maps arising from tetrahedron equation
Atsuo Kuniba
We survey the matrix product solutions of the Yang-Baxter equation obtained recently from the tetrahedron equation. They form a family of quantum matrices of generalized quantu…
Multispecies TASEP and combinatorial
Atsuo Kuniba, Shouya Maruyama, Masato Okado
We identify the algorithm for constructing steady states of the -species totally asymmetric simple exclusion process (TASEP) on site periodic chain by Ferrari and Martin wit…
Tetrahedron equation and generalized quantum groups
Atsuo Kuniba, Masato Okado, Sergey Sergeev
We construct -families of solutions of the Yang-Baxter equation from -products of three-dimensional and operators satisfying the tetrahedron equation. They are iden…