2020-07-14 08:19:07 -0500 received badge ● Popular Question (source) 2019-08-01 04:21:31 -0500 asked a question Automorphism group of edge symmetry I asked a similar question before, 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 $G$: G.automorphism_group().list()  However, the above way can only be used to the unweighted graph. So for example: G = matrix([[0,10,0], [10,0,1], [0,1,0]]) G1 = Graph(G, weighted = True) G1.show(edge_labels=True ) G.automorphism_group().list()  The result is: [(), (0,2)]  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? 2018-06-17 13:08:23 -0500 received badge ● Scholar (source) 2018-06-17 13:08:19 -0500 received badge ● Supporter (source) 2018-06-17 00:23:30 -0500 received badge ● Editor (source) 2018-06-16 18:01:45 -0500 received badge ● Student (source) 2018-06-16 18:00:37 -0500 asked a question About SymmetricGroupRepresentation() I am a new student in SAGE. I read the following discussion: evaluation of character of symmetric group and then also read the manual. However, I am still confused about some fundamental problem: (I cannot find these function in "Sage Reference Manual: Groups, Release 8.2". Are both new functions?). 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?