Poset Structure Concerning Cylindric Diagrams
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Published:2024-03-08
Issue:1
Volume:31
Page:
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ISSN:1077-8926
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Container-title:The Electronic Journal of Combinatorics
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language:
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Short-container-title:Electron. J. Combin.
Author:
Suzuki Takeshi,Nakada Kento,Toyosawa Yoshitaka
Abstract
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.
Publisher
The Electronic Journal of Combinatorics