2022-01-27 06:33:05 +0100 | commented answer | Find the longest word in a symmetric group which satisfies a certain property. @Max, thank you very much for your nice answer! |

2022-01-27 06:31:54 +0100 | commented answer | Find the longest word in a symmetric group which satisfies a certain property. @Max, thank you very much! |

2022-01-26 08:54:30 +0100 | received badge | ● Nice Answer (source) |

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2022-01-25 09:14:06 +0100 | edited answer | Find the longest word in a symmetric group which satisfies a certain property. I modified Max Alekseyev's answer. The result of the following codes agree with the result of the function LongestPerm i |

2022-01-25 09:11:54 +0100 | commented answer | Find the longest word in a symmetric group which satisfies a certain property. @Max, I checked some more examples and found that some of the results given by your codes do not agree with the function |

2022-01-25 09:10:03 +0100 | answered a question | Find the longest word in a symmetric group which satisfies a certain property. I modified Max Alekseyev's answer. The result of the following codes agree with the result of the function LongestPerm i |

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2022-01-24 21:55:40 +0100 | commented answer | Find the longest word in a symmetric group which satisfies a certain property. @Max, thank you very much! |

2022-01-24 21:55:19 +0100 | marked best answer | Find the longest word in a symmetric group which satisfies a certain property. Let $A, B$ be two list of equal length $k$, where $A$ is weakly increasing. For example, $A=[1, 1, 2, 3, 3, 4]$, $B=[12, 9, 10, 15, 15, 14]$. Define $m_{A,B}$ to be the multiset of pairs $[ A_i, B_i ]$, $i \in k$, (this is a multi-set of pairs of integers, not a list of pairs, so the order of pairs in $m_{A,B}$ does not matter). By a result in symmetric group, there is a unique element with maximal length (length of the reduced word) in the symmetric group $S_k$ ($k$ is the length of $A$) such that $m_{A,w(sorted(B))} = m_{A,B}$, where $sorted(B)$ is to sorted B such that it is weakly increasing, and the action of $w=s_{i_1} \cdots s_{i_m}$ on a list $L$ is defined by: $s_j(L)$ means exchanging the jth and j+1th elements of $L$, and for $w,w' \in S_k$, $w w'(L) = w(w'(L))$. There is a method to compute the longest word $w$ by checking all elements in $S_k$. But it takes a long time when $k$ is large. The following function works fine and returns correct result. In the example that we have Is there some method to compute $w$ faster (without checking all elements of $S_k$)? Thank you very much. |

2022-01-24 09:53:25 +0100 | edited question | Find the longest word in a symmetric group which satisfies a certain property. Find the longest word in a symmetric group which satisfies a certain property. Let $A, B$ be two list of equal length $k |

2022-01-24 09:52:25 +0100 | edited question | Find the longest word in a symmetric group which satisfies a certain property. Find the longest word in a symmetric group which satisfies a certain property. Let $A, B$ be two list of equal length $k |

2022-01-24 09:39:24 +0100 | edited question | Find the longest word in a symmetric group which satisfies a certain property. Find the longest word in a symmetric group which satisfies a certain property. Let $A, B$ be two list of equal length $k |

2022-01-24 09:39:00 +0100 | edited question | Find the longest word in a symmetric group which satisfies a certain property. |

2022-01-24 09:37:01 +0100 | edited question | Find the longest word in a symmetric group which satisfies a certain property. |

2022-01-24 09:36:13 +0100 | edited question | Find the longest word in a symmetric group which satisfies a certain property. Find the longest word in a symmetric group which satisfies a certain property. Let $A, B$ be two list of equal length, w |

2022-01-24 09:35:15 +0100 | asked a question | Find the longest word in a symmetric group which satisfies a certain property. Find the longest word in a symmetric group which satisfies a certain property. Let $A, B$ be two list of equal length, w |

2022-01-24 09:35:14 +0100 | asked a question | Find the longest word in a symmetric group which satisfies a certain property. Find the longest word in a symmetric group which satisfies a certain property. Let $A, B$ be two list of equal length, w |

2022-01-24 08:21:56 +0100 | commented answer | How to find a permutation which sends a given list to another given list in SageMath? @Max, thank you very much! |

2022-01-24 08:21:41 +0100 | commented answer | How to find a permutation which sends a given list to another given list in SageMath? @John, thank you very much! |

2022-01-23 20:14:34 +0100 | edited question | How to find a permutation which sends a given list to another given list in SageMath? How to find a permutation which sends a given list to another given list in SageMath? Given two list L1, L2, say L1=[1 |

2022-01-23 19:06:08 +0100 | commented question | How to find a permutation which sends a given list to another given list in SageMath? @John, $L1$ and $L2$ are lists. There could be repetition of elements in $L1$, $L2$. The numbers of occurrences of each |

2022-01-23 19:04:59 +0100 | commented question | How to find a permutation which sends a given list to another given list in SageMath? @John, $L1$ and $L2$ are lists. There could be repetition of elements in $L1$, $L2$. The numbers of occurrences of each |

2022-01-23 19:04:10 +0100 | commented question | How to find a permutation which sends a given list to another given list in SageMath? @John, $L1$ and $L2$ are lists (the order of the elements could not be changed). There could be repetition of elements i |

2022-01-23 19:02:19 +0100 | commented question | How to find a permutation which sends a given list to another given list in SageMath? @John, the result of $w$ is not unique. There is at least one $w$. I only need one $w$ such that $w(L1)=L2$. The only me |

2022-01-23 18:59:24 +0100 | commented question | How to find a permutation which sends a given list to another given list in SageMath? @John, thank you very much for your comments. I have edited the post. |

2022-01-23 18:58:26 +0100 | edited question | How to find a permutation which sends a given list to another given list in SageMath? How to find a permutation which sends a given list to another given list in SageMath? Given two list L1, L2, say L1=[1 |

2022-01-23 15:22:57 +0100 | edited question | How to find a permutation which sends a given list to another given list in SageMath? How to find a permutation which sends a given list to another given list in SageMath? Given two list L1, L2, say L1=[1 |

2022-01-23 15:21:30 +0100 | edited question | How to find a permutation which sends a given list to another given list in SageMath? |

2022-01-23 15:20:33 +0100 | edited question | How to find a permutation which sends a given list to another given list in SageMath? |

2022-01-23 15:17:09 +0100 | asked a question | How to find a permutation which sends a given list to another given list in SageMath? |

2022-01-23 15:17:07 +0100 | asked a question | How to find a permutation which sends a given list to another given list in SageMath? |

2022-01-23 15:07:15 +0100 | marked best answer | A question about definition of a polynomial ring. I am trying to define a polynomial ring as follows: It is ok with n=9, m=100. But when I change n, m to n=11, m=100. Then there is an error: ValueError: variable name 'x111' appears more than once I would like to have n=100, m=1000. How to solve this problem? Thank you very much. |

2022-01-23 15:05:49 +0100 | answered a question | How to find the element with maximal length in a double coset of a Coxeter group? The following codes work. def LongestPermInDoubleCosetWeylGroupGivenTypeRank(S1,w,S2,typ,rank): # typ='A', longest elem |

2022-01-23 10:29:07 +0100 | asked a question | A question about definition of a polynomial ring. A question about definition of a polynomial ring. I am trying to define a polynomial ring as follows: from sage.combina |

2022-01-21 20:47:21 +0100 | marked best answer | How to find the longest word in a subgroup of the symmetric group using Sage? Let $S_n$ be the symmetric group over $\{1,2,\ldots,n\}$. Let $J$ be a subset of $\{1,\ldots, n-1\}$ and let $W_J$ be the subgroup of $S_n$ generated by $s_j, j\in J \subset \{1, \ldots, n-1\}$, where $s_j$'s are simple reflections. How to find the longest word in $W_J$ in Sage? The following is some codes. Thank you very much. |

2022-01-21 20:47:21 +0100 | commented answer | How to find the longest word in a subgroup of the symmetric group using Sage? @FrédéricC, thank you very much for your very useful answer. Do you know how to find the unique element with maximal len |

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