Timeline for Combine two types of permutations in a Young diagram?
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Nov 5 at 13:24 | history | edited | Connor | CC BY-SA 4.0 |
added 54 characters in body
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| Nov 2 at 14:00 | history | edited | Connor | CC BY-SA 4.0 |
Added a more concrete question
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| Nov 2 at 13:56 | comment | added | Connor | I see. Actually, there the sum is the same for every cell. I edited it and added a concrete goal. | |
| Nov 2 at 13:55 | history | edited | Connor | CC BY-SA 4.0 |
Added a more concrete question
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| Nov 2 at 8:20 | comment | added | Peter Taylor | @Connor, on close reading your first comment contradicts itself and the question. If the aim is to minimise $\sum_r \max_c (\sigma_r(c) + \tau_c(r))$ then the answer to Sam's comment isn't "Yes", and the sum can't be as small as $|R| + 1$ in the case of a square, unless the square is $1 \times 1$. Please edit the question to express clearly what you actually want to ask about. | |
| S Oct 30 at 13:50 | history | suggested | eti902 |
Adding a tag
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| Oct 30 at 13:47 | review | Suggested edits | |||
| S Oct 30 at 13:50 | |||||
| Oct 29 at 12:27 | comment | added | Connor | Yes. Any non-trivial upper bound would be interesting. | |
| Oct 29 at 8:19 | comment | added | Peter Taylor | There's a trivial lower bound $\max(|R|, |C|) + 1$. It should be straightforward to adapt the argument for a square to achieve this lower bound. | |
| Oct 28 at 23:42 | comment | added | Connor | Yes, what you said sounds more concrete: let $t$ be a vector such that $t_i$ is the maximum sum of the two coordinates of a cell in row $i$. And the target is to minimize the $\ell_1$-norm of the vector $t$. | |
| Oct 28 at 20:50 | comment | added | Sam Hopkins | When you say, "[t]he goal of choosing those permutations is to make the sum of the row coordinate and column coordinate of each cell as small as possible," I guess you mean you want to minimize the maximum over all cells of this sum of row and column coordinate? | |
| Oct 28 at 19:16 | history | edited | LSpice | CC BY-SA 4.0 |
Capitalise title; TeX -> Unicode quotes
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| Oct 28 at 19:03 | history | asked | Connor | CC BY-SA 4.0 |