Timeline for LGV scheme for lattice paths that move in non-unit spatial positive steps
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 30, 2022 at 21:51 | vote | accept | Thomas Kojar | ||
| Dec 5, 2020 at 22:28 | comment | added | Thomas Kojar | that is what I am trying to get at. (The up-left motion doesn't make things any easier, they are equivalent as explained above.) I am searching for generalizations of LGV or SSYT dynamics. | |
| Nov 29, 2020 at 23:08 | comment | added | Sam Hopkins | I would suggest you study the network in Figure 2 and try to give a combinatorial interpretation of what (weighted) nonintersecting lattice paths in it are. | |
| Nov 29, 2020 at 22:49 | comment | added | Sam Hopkins | I don't understand what you mean by "two paths could intersect at a vertex not included in the weights" | |
| Nov 29, 2020 at 22:25 | comment | added | Thomas Kojar | The up-left is not really an issue actually because as mentioned in the post we can instead consider the weights $w(P(n),P(n+1)):= 1\{ P(n)\geq P(n+1) \}$. (as opposed to having weight 1). So we are back in the forwards and backwards motion but still non-unit steps. | |
| Nov 29, 2020 at 22:22 | comment | added | Thomas Kojar | So we might "miss" the intersection. In other words, two paths could intersect at a vertex not included in the weights. Therefore, we won't be able to do the involution switch as in the LGV proof. | |
| Nov 29, 2020 at 22:18 | comment | added | Thomas Kojar | The usual LGV doesn't apply because the weights are already fixed to have T-number of factors. | |
| Nov 29, 2020 at 16:28 | history | answered | Sam Hopkins | CC BY-SA 4.0 |