Timeline for Sum involving determinants of binomial coefficients, indexed by partitions
Current License: CC BY-SA 4.0
19 events
| when toggle format | what | by | license | comment | |
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| S Jul 10, 2020 at 15:04 | history | bounty ended | CommunityBot | ||
| S Jul 10, 2020 at 15:04 | history | notice removed | CommunityBot | ||
| Jul 4, 2020 at 19:32 | comment | added | Richard Stanley | See Problem 80 at math.mit.edu/~rstan/ec/ch7supp.pdf (version of 4 July 2020) and the solution at math.mit.edu/~rstan/ec/ch7suppsol.pdf. | |
| Jul 4, 2020 at 14:22 | vote | accept | Marcel | ||
| Jul 4, 2020 at 13:34 | comment | added | user35313 | @Marcel: Great. Done. | |
| Jul 4, 2020 at 13:33 | answer | added | user35313 | timeline score: 2 | |
| Jul 4, 2020 at 13:11 | comment | added | Marcel | @user61318 Yes, the factorization follows. Let me know if you are going to write an answer (otherwise I will write one myself) | |
| Jul 2, 2020 at 21:01 | comment | added | user35313 | @Marcel: OK! Does your claimed factorization follow though? | |
| Jul 2, 2020 at 20:45 | comment | added | Marcel | @user61318 Indeed, you are quite right and Lemma 9.1 in the paper you linked shows that my $E$ can be computed using an analogue of Cauchy-Binet. I would be happy to accept an answer with this content, if you want to write one. | |
| Jul 2, 2020 at 19:38 | comment | added | user35313 | @Marcel: Molev's original article on double Schurs describes them. There is no determinant there though Gessel-Viennot would do. Anyhow, see equation 53 of Damir Yeliussizov's paper: arxiv.org/pdf/1601.01581.pdf for your determinant for $A_{\lambda\rho}$. | |
| Jul 2, 2020 at 18:18 | comment | added | user35313 | If I didn't mess up, $A_{\lambda\rho}$ counts Molev's dual hook tableaux with shape $\lambda/\rho$ . Following Sam Hopkins' suggestion to put variables (two sets even) back might be good. | |
| Jul 2, 2020 at 16:44 | comment | added | user35313 | Very vague comment. I wonder if your $E_{\lambda,\nu}$ comes from Cauchy-Binet applied to a minor of an appropriate product of matrices. Skew Schurs can be recognized as minors of a matrix (think Jacobi-Trudi). I think your $A_{\lambda\rho}$s can also be recognized as minors of an appropriate infinite matrix. Perhaps the product of matrices has nice structure. | |
| S Jul 2, 2020 at 13:10 | history | bounty started | Marcel | ||
| S Jul 2, 2020 at 13:10 | history | notice added | Marcel | Draw attention | |
| Jun 30, 2020 at 14:11 | comment | added | Sam Hopkins | An obvious but probably unhelpful suggestion is to try to put variables $x_i$ back into the equation. | |
| Jun 30, 2020 at 14:09 | history | edited | Marcel | CC BY-SA 4.0 |
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| Jun 30, 2020 at 14:00 | comment | added | Suvrit | What is the actual question then in this case? It seems no "formal" question has been stated in the post.... | |
| Jun 30, 2020 at 13:05 | history | edited | Marcel | CC BY-SA 4.0 |
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| Jun 30, 2020 at 13:00 | history | asked | Marcel | CC BY-SA 4.0 |