Timeline for Correspondence between $SBT (n)$ and $W(B_n)$
Current License: CC BY-SA 3.0
17 events
| when toggle format | what | by | license | comment | |
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Oct 11, 2016 at 10:57 | history | edited | Amritanshu Prasad | CC BY-SA 3.0 |
deleted 66 characters in body
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| Oct 11, 2016 at 10:31 | history | edited | Amritanshu Prasad | CC BY-SA 3.0 |
Fixed error in code output example $W(B_2)$.
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| Oct 11, 2016 at 8:04 | comment | added | bing | Let us continue this discussion in chat. | |
| Oct 11, 2016 at 8:01 | comment | added | bing | @ Amritanshu Prasad Thank you very much. | |
| Oct 11, 2016 at 7:49 | comment | added | Amritanshu Prasad | Each line of output is an element of $W(D_2)$, followed by a pair of bitableaux. For example $[2, -1]$ is the element $\begin{pmatrix}1 & 2 & -1 &-2\\2&-1&-2&1\end{pmatrix}$. In general, I am simply listing the first $n$ elements of your second row. Then enclosed in parentheses are two domino tableaux, listed by row. So $[[1, 2, 2], [1]]$ represents the tableau $\begin{matrix}1&2&2\\1&&\end{matrix}$. | |
| Oct 11, 2016 at 7:20 | comment | added | bing | @ Amritanshu Prasad I have a question. How to understand the elements of $W(B_2)$ as I wrote ? For example, what is [1, 2] ([[1, 2, 2], [1]], [[1, 2, 2], [1]])? | |
| Oct 11, 2016 at 7:07 | vote | accept | bing | ||
| Oct 11, 2016 at 7:06 | comment | added | Amritanshu Prasad | There are two possible (mutually transpose) conventions for representing permutations by matrices. The one I chose is the more commonly used one (used by Knuth). | |
| Oct 11, 2016 at 7:04 | comment | added | bing | @ Amritanshu Prasad Thank you very much. I will send you an E-mail. | |
| Oct 11, 2016 at 7:01 | vote | accept | bing | ||
| Oct 11, 2016 at 7:05 | |||||
| Oct 11, 2016 at 6:58 | comment | added | Amritanshu Prasad | Yes, I added more details just now, along with the $W(B_2)$ examples and Sage code. Do let me know if you have trouble with the code. My e-mail address is available from my webpage, which is linked in my profile. | |
| Oct 11, 2016 at 6:57 | history | edited | Amritanshu Prasad | CC BY-SA 3.0 |
Added Sagecode, and comparison with Brian Hopkins answer.
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| Oct 11, 2016 at 6:50 | comment | added | bing | Thank you very much. But I think that \begin{align*} w = \begin{pmatrix} 1 & 2 & 3 & -1 & -2 & -3\\ 2 & -1 & -3 & -2 & 1 & 3 \end{pmatrix} \in W(B_3) .\end{align*} How to define a pair of partial permutations (A,B)? For $w$, could we define $$ A = \begin{pmatrix} 0 & 1 & 0\\ 0 & 0 & 0\\ 0 & 0 & 0\end{pmatrix}, \quad B = \begin{pmatrix} 0 & 0 & 0\\ 1 & 0 & 0\\ 0 & 0 & 1\end{pmatrix}? $$ | |
| Oct 11, 2016 at 4:24 | history | edited | Amritanshu Prasad | CC BY-SA 3.0 |
Added domino tableaux example.
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| Oct 11, 2016 at 3:07 | history | edited | Amritanshu Prasad | CC BY-SA 3.0 |
added 18 characters in body
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| Oct 10, 2016 at 16:12 | history | answered | Amritanshu Prasad | CC BY-SA 3.0 |