![巡回置換の共役変換
𝜏 ∈ 𝑆 𝑛 = 𝜎: 𝑛 → 𝑛 | 𝐵𝑖𝑗𝑒𝑐𝑡𝑖𝑜𝑛 , 𝑛 = 1,2, … , 𝑛 − 1, 𝑛
𝜏 [𝑛] = 𝑛 , 𝑘 ∈ 𝑛
𝜏 𝑖1, 𝑖2, … , 𝑖 𝑟 𝜏−1 𝜏 𝑘 = 𝜏 𝑖1, 𝑖2, … , 𝑖 𝑟 𝑘 =
𝜏 𝑖𝑗+1 mod 𝑟 𝑖𝑓 𝑘 = 𝑖𝑗 ∈ {𝑖1, 𝑖2, … . , 𝑖 𝑟}
𝑘 𝑂𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
∴ 𝜏 𝑖1, 𝑖2, … , 𝑖 𝑟 𝜏−1
= 𝜏 𝑖1 , 𝜏 𝑖2 , … , 𝜏(𝑖 𝑟)](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
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Conjugate cyclic permutation
- 1. Conjugate cyclic permutation June 15, 2016 (Wednesday) 13:46 (Japan time) Nagaoka University of Technology M1 Tamura Takumi
- 2. 巡回置換の共役変換 𝜏 ∈ 𝑆 𝑛 = 𝜎: 𝑛 → 𝑛 | 𝐵𝑖𝑗𝑒𝑐𝑡𝑖𝑜𝑛 , 𝑛 = 1,2, … , 𝑛 − 1, 𝑛 𝜏 [𝑛] = 𝑛 , 𝑘 ∈ 𝑛 𝜏 𝑖1, 𝑖2, … , 𝑖 𝑟 𝜏−1 𝜏 𝑘 = 𝜏 𝑖1, 𝑖2, … , 𝑖 𝑟 𝑘 = 𝜏 𝑖𝑗+1 mod 𝑟 𝑖𝑓 𝑘 = 𝑖𝑗 ∈ {𝑖1, 𝑖2, … . , 𝑖 𝑟} 𝑘 𝑂𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 ∴ 𝜏 𝑖1, 𝑖2, … , 𝑖 𝑟 𝜏−1 = 𝜏 𝑖1 , 𝜏 𝑖2 , … , 𝜏(𝑖 𝑟)