Timeline for Formula for number of edges in Hasse diagram of Young's lattice interval
Current License: CC BY-SA 4.0
5 events
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| Mar 4, 2019 at 19:53 | comment | added | Sam Hopkins | @RichardStanley: thanks, good to know there is likely not a nice answer. (A kind of answer is given by Theorem 3.4 of cambridge.org/core/journals/forum-of-mathematics-sigma/article/… but it involves summing over all corners of the skew shape and so is pretty unwieldy.) | |
| Mar 4, 2019 at 19:47 | comment | added | Richard Stanley | You are asking for the number of skew plane partitions of shape $\lambda/\mu$ with parts $1,2,3$ and with exactly one part equal to 2. This doesn't fit naturally into what is known about plane partitions, so I wouldn't be surprised if the problem does not have a nice solution. | |
| Mar 4, 2019 at 17:56 | history | edited | Sam Hopkins |
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| Mar 3, 2019 at 18:50 | comment | added | Sam Hopkins | (In fact the Kreweras/MacMahon formula is for the number of $m$-multichains of this interval, but we can take $m=1$.) | |
| Mar 3, 2019 at 18:43 | history | asked | Sam Hopkins | CC BY-SA 4.0 |