Tom:I like the name!
I was going to suggest that the five-position situation should be considered both before and after the move. However, on reflection, it is very often the case that the fact of a capture is much more important than whether an empty triangle is made at the same time. So I suggest that it should be assumed that no capture is made for a Spightonian. This is pretty much what you have done, except that it would eliminate the final Spightonian, leaving 20.
(Sebastian:) You are right that when captures come into play, the distinction about what was there before becomes a bit moot. We could write this in the introducting paragraph. However, I would rather keep the name "Spightonian" for all 21 geometrically possible patterns - just as the periodic table ends with elements that hardly ever are realized.
Tom: Is there a reason that you haven't included the 'throw in'?
(Sebastian:) "throw in" seems to refer more to a tactical purpose of a move rather than a specific move shape itself. Could you draw the Spightonian for what you have in mind?
(Sebastian:) How do we include moves at the edge of the board in this list?
Can we replace the border with mirrored points like this?
I (Malcolm) only counted 20 diagrams. Also, I didn't see the following diagrams :
Maybe I'm missing something.
(Sebastian:) The _ripped keima_ is a subclass of the tap (touching 1 enemy and 1 friend). But the _ripped keima plus one stone_ belongs to a class which I did indeed not list: touching 1 enemy and 2 friends. There are 6 such classes; I only listed classes that either already have names, or that contain important subclasses. There are more diagrams than listed classes, because some of them illustrate subclasses.
I see how it is confusing that I didn't mention that the page doesn't list all classes, so let's prepare a table. There are 15 different multisets with cardinality 4 of
,
and empty spaces. 6 of these (such as the tap and the thrust) have 2 different possible arrangements for the same number of stones. (These are the ones in which at least one element - either
,
, or empty space - has exactly 2 memberships.) I will call the two related arrangements "ortho-" and "para-", in analogy to the nomenclature for
arene substitution patterns. In ortho-patterns, the dual-members occupy orthogonally adjacent places; in para-patterns, they occupy opposite places.
This gives us the following table of all possible classes. I indicated the unnamed patterns with systematic names in parentheses. If there is only one name in a cell, then there is no distinction between ortho- and para- patterns.
(arrangement) \
| 0 | 1 | 2 | 3 | 4 | ----------------------+---------------+---------------+---------------+---------------+--------------+ 0 (ortho-) | untouched | touch | carve | (3e0f) | gouge | 0 (para-) | | | general wedge | | | ----------------------+---------------+---------------+---------------+---------------+--------------+ 1 (ortho-) | narabi | tap | chop | sashikomi | 1 (para-) | | thrust | impinge | | ----------------------+---------------+---------------+---------------+---------------+ 2 (ortho-) | straddle | (1e2f.o) | (2e2f.o) | 2 (para-) | botsugi | (1e2f.p) | division | ----------------------+---------------+---------------+---------------+ 3 | (0e3f) | (1e3f) | ----------------------+---------------+---------------+ 4 | fill | ----------------------+---------------+