does somebody know if there is any software for visualizing very large posets? (like those in page 27 of this notes of Guenter Ziegler). They may arise (as in that text) by considering the face lattices of high dimensional polytopes. Thanks!
5 Answers
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I feel certain that Ziegler's Fig. 2.1 below (to which I assume you are referring?)
was just drawn "by hand"
in a generic drawing program,
such as Adobe Illustrator, or xfig.
(p.643 = 27th page of notes linked by Camilo)
This is probably not what you want, but Mathematica (via Combinatorica) can draw Hasse diagrams.
See, e.g., this link for how to accomplish this.
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$\begingroup$ Thanks!. Yep, those where the ones I meant. I thought they could have been generated "exactly", upon input of a poset, so that for very large posets they look smoothed out, instead of like a tangle of hair. $\endgroup$ Commented Dec 1, 2011 at 10:04
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John Stembridge's site containing Maple packages for symmetric functions, posets, root systems, and finite Coxeter groups could be helpful.
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2$\begingroup$ In particular, $\mathtt{plot\_poset}$ in the $\mathtt{posets}$ package will automatically draw a Hasse diagram of a poset. math.lsa.umich.edu/~jrs/software/posetshelp.html#plot_poset $\endgroup$ Commented Jul 27, 2015 at 14:38
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David Cook, Sonja Mapes and I have a package for Macaulay 2 which draws pictures of posets, either with or without node labels. It will produce the TikZ code to include these in papers as well.
How large though is "very large"? While there are a number of built-in enumerators in our package (lcm lattices, hyperplane arrangement lattices, noncrossing partition lattices, etc.) which can produce fairly large posets quickly, the only limitation might be how you're storing or inputting these posets.
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$\begingroup$ The package is still in development, but if you're familiar with Macaulay 2 and interested, the Posets.m2 file can be downloaded at: dl.dropbox.com/u/4621422/Posets.m2 It does make use of the Graphs.m2 package as well, which was worked on extensively this summer at the IMA workshop: dl.dropbox.com/u/4621422/Graphs.m2 $\endgroup$ Commented Nov 30, 2011 at 20:39
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$\begingroup$ Thanks, I will have a look. Very large was such that it may be more illuminating to draw the poset as a shaded area, like in the figures Joseph posted (say, over 100 elements?). Though I guess in this case such illustrations could be obtained from the rank function alone. $\endgroup$ Commented Dec 1, 2011 at 10:12
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I'm seeing this question very late, but have two possibly useful suggestions for drawing posets:
My favorite way to automatically draw large graphs with unknown structure is GraphViz. See http://www.graphviz.org/
With some work, this can be made to give poset diagrams. That's one of the good options for output of Stembridge's Poset package for Maple, as mentioned in one of the other answers. (But GraphViz is open source software, which seems like a significant advantage to me.) Looking at the source code of Stembridge's package might be a good place to start in figuring out which GraphViz options to look at.GAP with the XGap (for Unix/Xwindows) or my own Gap.app (for Mac) front-end has code which allows manipulating Hasse diagrams of posets. I have found it useful for making good diagrams of small to medium size posets. I realize that the question asks about large posets, but include this for completeness.
For good results, GAP requires you to specify the position of the vertices (and automatically draws the edges for you), so it helps if you have some idea of the structure of the poset.
(I can share an example or two of presenting poset diagrams with GAP, if it would be helpful.)
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Curtis Greene et al. have a nice package at http://ww3.haverford.edu/math/cgreene.html.