Séminaire Lotharingien de Combinatoire, 93B.157 (2025), 12 pp.

Kento Nakada, Takeshi Suzuki and Yoshitaka Toyosawai

Colored Hooks and Poset Structure of Cylindric Diagrams

Abstract. Cylindric diagrams admit structures 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 finite order ideals of a cylindric diagram is described as a weak right Bruhat interval of the affine Weyl group.


Received: November 15, 2024. Accepted: February 15, 2025. Final version: April 1, 2025.

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