The Cube Recurrence

The Multidimensional Cube Recurrence

We introduce a recurrence which we term the multidimensional cube recurrence, generalizing the octahedron recurrence studied by Propp, Fomin and Zelevinsky, Speyer, and Fock and Goncharov and the three-dimensional cube recurrence studied by Fomin and Zelevinsky, and Carroll and Speyer. The states of this recurrence are indexed by tilings of a polygon with rhombi, and the variables in the recurrence are indexed by vertices of these tilings. We travel from one state of the recurrence to another by performing elementary flips. We show that the values of the recurrence are independent of the order…

Periodicity and integrability for the cube recurrence

Zamolodchikov periodicity is a property of $T$- and $Y$-systems, arising in the thermodynamic Bethe ansatz. Zamolodchikov integrability was recently considered as its affine analog in our joint work with P. Pylyavskyy. Here we prove periodicity and integrability for similar discrete dynamical systems based on the cube recurrence, also known as the discrete BKP equation. The periodicity part was conjectured by Henriques in 2007.

Horadam 立方体

Horadam cubes

本文提出并研究了一个新的三参数图族 Horadam 立方体，其顶点数满足 Horadam 递推，并证明了它保留 Fibonacci 和 metallic 立方体的许多良好性质，同时分析了其分解、度量、计数性质及 Hamiltonian 路径与圈的存在性。

关于Gelfand-Zetlin多胞体的面数

On the number of faces of Gelfand-Zetlin polytopes

本文通过研究Gelfand-Zetlin多胞体到立方体的线性投影，建立其f-多项式的递推关系，并由此给出若干单参数族的f-多项式和h-多项式的显式公式。