Geodesic
Poset structure concerning cylindric diagrams
Takeshi Suzuki1 ; Kento Nakada ; Yoshitaka Toyosawa
1Associated Professor
The electronic journal of combinatorics, Tome 31 (2024) no. 1
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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.
DOI : 10.37236/12205
Classification : 05E10, 06A11, 20F55
Mots-clés : infinite \(d\)-complete posets with natural ordering, set of order ideals of a cylindric diagram

Takeshi Suzuki  1   ; Kento Nakada    ; Yoshitaka Toyosawa 

1 Associated Professor 
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     author = {Takeshi Suzuki and Kento Nakada and Yoshitaka Toyosawa},
     title = {Poset structure concerning cylindric diagrams},
     journal = {The electronic journal of combinatorics},
     year = {2024},
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     number = {1},
     doi = {10.37236/12205},
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Takeshi Suzuki; Kento Nakada; Yoshitaka Toyosawa. Poset structure concerning cylindric diagrams. The electronic journal of combinatorics, Tome 31 (2024) no. 1. doi: 10.37236/12205

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