Solutions of Reeder's Puzzle

2015/11/10 by Zachi Evenor, Evenor, Zachi
Mathematics · #05E15 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #math.CO #msc:05E15

paper · pdf · doi:10.48550/arxiv.1511.03069

openalex publication_date 2015/11/10 · arxiv created 2017/06/19 · arxiv updated 2017/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we consider the generalized Reeder's puzzle, introduced by Reeder in 2005 and generalized by Borovoi and Evenor in 2016. We give a detailed solution of the puzzle for the graphs of Dynkin diagrams and affine Dynkin diagrams. We find the number of equivalence classes in each case. We also discuss more general graphs, and prove the main theorem about graphs (simply-laced trees) that contain E₆ as a subgraph.

Citations

• Lit-only sigma-game and its dual game

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