Talk:Plane partition

Section on symmetries needs expanding
There's a substantial literature on the enumeration of plane partitions according to various symmetries. The stubby section I started should be expanded to say something about this!

Also, there's much more that should be added to this article: e.g., more refined enumerations than the ones given, connections to symmetric function theory, etc. Joel B. Lewis (talk) 00:59, 12 June 2012 (UTC)

Large tables added to article
recently added the following large tables to the article, in a first section (immediately following the lead) called "Overview":

I have a couple of concerns about this that I'd like to discuss.

First, the placement seems really unfortunate: no one who does not understand already the text in the article could possibly understand these tables, and they are the very first thing that one sees after the introduction. So, if they are to be kept, I would propose moving them to the very end of the article, rather than the beginning, or splitting them apart from each other.

Second, I am a skeptic of lists and tables in general, and this seems to me like a good example of the reason why: in what way is this a better presentation than prose paragraphs with illustration? I find the format cramped and difficult to read, and there is no obvious sorting here that would make a table particularly helpful or clear. The tables seem to be as large or larger than the text they summarize. So I am inclined to remove them.

On both points, I would be very willing to hear counterarguments/discussion. --JBL (talk) 13:09, 20 April 2018 (UTC)


 * Thanks you for taking time to read through my article and giving constructive feedback! I totally agree with you that the tables better fit on the end for a clearer structure of the article. I also share your view on the second statement. Lists and tables of this size are really unwieldy. I still decided to include the tables, as I thought a table would be handy to look up, especially for people who are familar with this topic. The tables are expendable in my view, because they're just a summary of the article.Sophie Hofmanninger (talk) 19:09, 22 April 2018 (UTC)

Also I should say that the addition of the pictures of the symmetry classes is wonderful, thanks very much for that! --JBL (talk) 13:42, 20 April 2018 (UTC)

Split proposal
I think this article now is much too heavy on symmetry classes and too light the plane partitions themselves. This often happens when people ignore WP:NOTTEXTBOOK and WP:IINFO. Since the editor made so much effort, I propose a split of the article into two: "Plane partition" and "Symmetry classes of plane partitions", with both the sections and the catalogue above moving to a new place. I plan to make the split myself within a week unless I hear objections from other editors. Mhym (talk) 22:40, 22 April 2018 (UTC)


 * I don't think that it violates WP:NOTTEXTBOOK. It lists quite concisely the notions and facts/formulas. There is no "teaching" involved. (Unfortunately, there is much worse out there...) What would remain if all symmetry related contents are (re)moved to elsewhere? Only sections 1 & 2. This makes about 2 screens of text. Well, maybe this is sufficient for a "unit of knowledge". I think there are many pages which are much longer... but why not, if you want to divide it up... IMHO not necessary, but would be also OK for me. &mdash; MFH:Talk 21:26, 6 October 2018 (UTC)


 * I agree. Enumeration of symmetry classes is a major aspect of the study of plane partitions.  What this article could use is more discussion of other aspects of their study in addition to the enumeration of symmetry classes.  --JBL (talk) 18:54, 7 October 2018 (UTC)

Symmetric (but not necessarily cyclically or totally symmetric) self-complementary plane partitions?
Looking at the various special categories of plane partitions, one seems to be missing: those that are both the "normal" kind of symmetric and self-complementary but not (necessarily) cyclically symmetric (and thus not (necessarily) totally symmetric). Those that are not cyclically or totally symmetric definitely exist. Like if, in the matrix given in the article as an example of a totally symmetric self-complementary plane partition, $\pi$3,3 were changed from 5 to 4 and π4,4 were changed from 1 to 2 (or, in the graph, the block (3,3,5) were removed but the block (4,4,2) added), the resulting plane partition would still be both the "normal" kind of symmetric (everything I changed was on the diagonal i = j) and self-complementary (the (4,4,2) block would fill the gap formed by removing the (3,3,5) block in the complementary plane partition) but would no longer be cyclically or totally symmetric ((3,5,3) (5,3,3) would be elements of the partition but not (3,3,5), and a (4,4,2) would be an element of the partition but neither (2,4,4) nor (4,2,4) would be).

Should there be a section on that class of plane partitions? Have any formulas been conjectured (or better yet, proven) for the number of unique ("normally") symmetric self-complementary plane partitions of dimension $$(r,r,t)$$ or $$(2r,2r,2t)$$? Like all the other sets, this one would include plane partitions with additional symmetry, but I wanted to show in the previous paragraph that partitions with the properties I was talking about without additional symmetry existed. Numerically that set would seem to optimally be called $$N_6$$, with the set of cyclically symmetric self-complementary plane partitions being renumbered from $$N_6$$ to $$N_7$$ and the set of totally symmetric self-complementary plane partitions being renumbered from $$N_7$$ to $$N_8$$.

I can't be the only one who has noticed this omission. I'd be interested to know what others' thoughts were on this. Kevin Lamoreau (talk) 21:56, 20 February 2021 (UTC)


 * There are 10 inequivalent symmetry problems for plane partitions -- see . So, there are 3 missing from the present article, including the one you mention. --JBL (talk) 22:08, 20 February 2021 (UTC)


 * Interesting. I remember thinking of the self-complementary category as "the odd one" (the one you add to the other 4 including the general one to get 8 categories), but now the cyclically symmetric category seems like the one (and the only one) that results in a simple multiplication by 2.  You can have 0, 1 or 3 of (normally) symmetric (congruent to its transpose), self-complementary (congruent to its complement) and the complement being congruent to the transpose, which is the missing category I wasn't aware of.  The zero plus any three of the one's plus all three gives you five categories, and being cyclically symmetric or not gives you 10.  Thanks for that info.  Kevin Lamoreau (talk) 00:48, 14 March 2021 (UTC)


 * I should say, for purposes of categories of plane partitions with possible added symmetry, you could have zero, one or all three of (normally) symmetric, self-complimentary and complement=transpose required in the category while having all categories be unique (requiring any two of those would be the same as requiring all three). That zero plus any of the three one's plus all three gives you five categories, and whether or not you require the partition to be cyclically symmetric results in a multiplication by 2 to get 10 categories. Kevin Lamoreau (talk) 19:42, 25 April 2021 (UTC)

Soma cube pieces
Exhaustively, how many plane partitions do the pieces of a Soma cube have? kencf0618 (talk) 22:02, 26 September 2023 (UTC)