Poset Structure Concerning Cylindric Diagrams

  • Takeshi Suzuki
  • Kento Nakada
  • Yoshitaka Toyosawa


Cylindric diagrams admit the structure of infinite $d$-complete posets with natural ordering. The purpose of this paper is to provide a realization of a cylindric diagram as a subset of an affine root system of type A via colored hook lengths and to present several characterizations of its poset structure. Furthermore, the set of order ideals of a cylindric diagram is described as a weak Bruhat interval of the affine Weyl group.

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