Skip to main content

Formula to Partitions

For the benefit of my (2) readers, here is the process of going from the chemical formula to the partitions, and what this actually means.

So, the list of numbers at the bottom (the partition) is the simplest possible representation of the attachment points for each atom fragment.

Oh, and the python code for generating partitions for is here - it is basically a straight copy of the code from the book "Combinatorial Algorithms : Generation, Enumeration, and Search", which I highly recommend - a good balance of maths and computer science.

Comments

Rich Apodaca said…
Gilleain, I've been following this series of graphics with interest. Unfortunately, I'm not quite sure what problem it's related to (I feel like I missed something). This seems to be related to structure enumeration, but I'm not sure.

What do you think about writting a post that summarizes the problem (or links to the summary), and then how these graphics get you closer to the solution?

Also, is it possible to change your comment settings to allow comments by leaving a name/email/url combination? Not everyone has a google or openid account.
gilleain said…
Hi Rich,

Heh. It's mainly because I know that most readers already know what I am trying to do, and only need to know how far I have got, and what path I have taken.

Yes, you guessed right - it is structure generation (although enumeration would also be nice).

I changed the comment settings to 'anyone' as there is no intermediate between that and openID/google.

Popular posts from this blog

Adamantane, Diamantane, Twistane

After cubane, the thought occurred to look at other regular hydrocarbons. If only there was some sort of classification of chemicals that I could use look up similar structures. Oh wate, there is . Anyway, adamantane is not as regular as cubane, but it is highly symmetrical, looking like three cyclohexanes fused together. The vertices fall into two different types when colored by signature: The carbons with three carbon neighbours (degree-3, in the simple graph) have signature (a) and the degree-2 carbons have signature (b). Atoms of one type are only connected to atoms of another - the graph is bipartite . Adamantane connects together to form diamondoids (or, rather, this class have adamantane as a repeating subunit). One such is diamantane , which is no longer bipartite when colored by signature: It has three classes of vertex in the simple graph (a and b), as the set with degree-3 has been split in two. The tree for signature (c) is not shown. The graph is still bipartite accordin

Király's Method for Generating All Graphs from a Degree Sequence

After posting about the Hakimi-Havel  theorem, I received a nice email suggesting various relevant papers. One of these was by Zoltán Király  called " Recognizing Graphic Degree Sequences and Generating All Realizations ". I have now implemented a sketch of the main idea of the paper, which seems to work reasonably well, so I thought I would describe it. See the paper for details, of course. One focus of Király's method is to generate graphs efficiently , by which I mean that it has polynomial delay. In turn, an algorithm with 'polynomial delay' takes a polynomial amount of time between outputs (and to produce the first output). So - roughly - it doesn't take 1s to produce the first graph, 10s for the second, 2s for the third, 300s for the fourth, and so on. Central to the method is the tree that is traversed during the search for graphs that satisfy the input degree sequence. It's a little tricky to draw, but looks something like this: At the top

1,2-dichlorocyclopropane and a spiran

As I am reading a book called "Symmetry in Chemistry" (H. H. Jaffé and M. Orchin) I thought I would try out a couple of examples that they use. One is 1,2-dichlorocylopropane : which is, apparently, dissymmetric because it has a symmetry element (a C2 axis) but is optically active. Incidentally, wedges can look horrible in small structures - this is why: The box around the hydrogen is shaded in grey, to show the effect of overlap. A possible fix might be to shorten the wedge, but sadly this would require working out the bounds of the text when calculating the wedge, which has to be done at render time. Oh well. Another interesting example is this 'spiran', which I can't find on ChEBI or ChemSpider: Image again courtesy of JChempaint . I guess the problem marker (the red line) on the N suggests that it is not a real compound? In any case, some simple code to determine potential chiral centres (using signatures) finds 2 in the cyclopropane structure, and 4 in the