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- W575942943 abstract "Let S={s_1,s_2,...,s_n} be a finite set and m be a function with m:S×S→N∪{∞} satisfying m(s,s)=1 and m(s,s')=m(s',s)∈ {2,3} for distinct s,s'∈S. The set S is associated with the graph, also denoted by S, with the vertex set S and the edge set {ss'|m(s,s')=3}. A simply-laced Coxeter group W_S associated with (S,m) is the group generated by S subject to the relations (s,s')^{m(s,s')} for s,s'∈ S. We consider a homomorphism σ:W_S→GL(R^n), which is referred as canonical representation of W_S, where GL(R^n) is the group of invertible linear transformations of R^n into itself. We consider the canonical representation σ of W_S into R^n and use its dual representation σ* to show that W_S is isomorphic to the symmetric group S_{n+1} if the graph S is an n-vertex path. The matricesσ*(W_S)have integral coefficients. The left multiplication of these matrices modulo 2 on the n-dimensional space {F_2}^n over a binary field is usually called the lit only σ-game on the graph S in literatures. In the special case when S is a 3-vertex cycle, we determine the subgroup G of S W with σ*(G)={I} (mod2) ." @default.
- W575942943 created "2016-06-24" @default.
- W575942943 creator A5082560094 @default.
- W575942943 date "2011-01-01" @default.
- W575942943 modified "2023-09-25" @default.
- W575942943 title "Lit-only σ-games的代數結構" @default.
- W575942943 doi "https://doi.org/10.6842/nctu.2011.00281" @default.
- W575942943 hasPublicationYear "2011" @default.
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