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2019-08-01 04:21:31 -0500 | asked a question | Automorphism group of edge symmetry I asked a similar question before, https://ask.sagemath.org/question/427... I am curious that is there any similar function for finding "edge symmetry"? Note: the link I provided is for "node symmetry" in a network (graph). |

2018-06-27 20:22:14 -0500 | asked a question | Automorphism group of weighted graph I know we can use sage to find the group of automorphisms of a graph $G$: However, the above way can only be used to the unweighted graph. So for example: The result is: However, this result is not correct (correct for unweighted case). This is because $AD\neq DA$, where $$D = \begin{bmatrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{bmatrix},$$ which is a permutation matrix and $$A = \begin{bmatrix} 0 & 10 & 0 \\ 10 & 0 & 1 \\ 0 & 1 & 0\end{bmatrix},$$ which is an adjacency matrix. Can we use SAGE to find the group of automorphisms of a graph? |

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2018-06-16 18:00:37 -0500 | asked a question | About SymmetricGroupRepresentation() I am a new student in SAGE. I read the following discussion: However, I am still confused about some fundamental problem: About `SymmetricGroupRepresentation(partition, implementation='specht', ring=None, cache_matrices=True)` I am confused about "partition". Suppose for $S_3$, and partition $=[2,1]$. What does it mean? (It seems $[1,2]$ is not valid) About `spc = SymmetricGroupRepresentation([2,1], 'specht') spc.representation_matrix(Permutation([1,2,3]))` When I use `spc.representation_matrix(Permutation([1,2]))` error pops out. However, as far as I know, $(1,2)$ is a valid permutation, which represent the matrix representation: $$\begin{bmatrix}0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1\end{bmatrix}$$
However, if I use 'orthogonal' instead of 'specht', the answer becomes $$\begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}$$ But I test another permutation: $[1,2,3]$, the answer is the same. However, $[1,2]$ and $[1,2,3]$ are in the different conjugacy classes; they should not have the same character. I cannot find "Permutation" in "Sage Reference Manual: Group". Where can I find this function? |

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