Timeline for Why were plane partitions invented?
Current License: CC BY-SA 2.5
5 events
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| Feb 26, 2011 at 20:00 | comment | added | Greg Kuperberg | @Richard I'm left thinking that my answer just isn't that great. Your books seem incredibly careful in general with citations and history. I said parenthetically that "some of these connections were only cleaned up decades later", and it seems possible now that this last remark is more true than everything else that I said. | |
| Feb 26, 2011 at 19:40 | comment | added | Richard Stanley | I researched a lot of this history for the Notes section of Chapter 7 of Enumerative Combinatorics, vol. 2. I write that the first statement that Kostka numbers count semistandard tableaux (and so far as I know the first appearance of such tableaux in the literature) was given by D. E. Littlewood in 1937, well after the work of MacMahon. I would be interested in any corrections to these Chapter 4 Notes. | |
| Feb 26, 2011 at 6:47 | comment | added | Greg Kuperberg | Yes, there is an injection from all semistandard tableaux to all plane partitions, since plane partitions are weakly decreasing in both directions. But I had in mind "special case" in a more bijective sense. If you take the plane partitions in an $a \times b \times c$ box, they are bijective with semistandard tableaux with a rectangular shape. However, semistandard tableaux with some other partition shape, and a finite alphabet, are not bijective with any very convenient class of plane partitions. | |
| Feb 25, 2011 at 20:19 | comment | added | Sheikraisinrollbank | Nitpick: "...plane partitions are a special case of semistandard tableaux..."? I would have thought it's the other way round: semistandard tableaux (or "column-strict tableaux") are plane partitions with the property that column height strictly decrease from top to bottom. | |
| Feb 25, 2011 at 20:11 | history | answered | Greg Kuperberg | CC BY-SA 2.5 |