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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