Alternating generation depth partition

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Andrej

We have made an interesting discovery about Australian kinship and here is an example attached.

Marriages between adjacent generations are not allowed. Marriage has to be within the same generation, defined by links between siblings those of marriage, or within alternating generations, +2/-2

So imagine that we have Relation 1 to male or husband's parent as in this file and 2 to wife's or a woman's parent.

Now if you transpose Relation 2 and take the relational composition of 1 and 2inverse to get Z=sisters these nodes in a Pgraph will contain the ZsHusbands, and these will form directed chains.

Compute the large components of these chain sets.

Then take each component and compute within each the grandchild/grandparent relations as the composition of (1 and 2) with (1 and 2), resulting in a directed chain of length 2. Go to Draw and use these to sort generations using Depth/Acyclic and putting the nodes with no children at the bottom. These are the layers of alternating generations. Give each such layer a distinct partition color from all other such layers.

Keep these partitions and show them superimposed on the depth/generations.

Question is: do these two methods of computing generations roughly correspond? If not:

Compute the (number of) parent/child relations between the alternating generation partitions. If they form a depth partion, renumber the AG generations accordingly.

[edit] Alternate statement

An algorithm to find generations in section systems with marriages between +2/-2 generation relatives must first find whether there are several components connected through sibling-in-law chains, and if not, to report that there are no alternating generations and thus no sections. Then these components would be ordered internally and externally by their parent-child ties, which can only be an even number of generations deep in a section system. If this intersection of parental ordering and potentially alternating generations do not sort out in a way so that parent-child links traverse an odd number of generations starting from parent or child, then there are no alternating generations and no sections)

[edit] Question

Does it look to you like this is computable? If there were no +2/-2 pgraph marriages and no marriages in adjacent generations then the R1 composition with R2inverse would create separate components whose partition would correspond to generations. WikiSysopWikiSysop 15:26, 9 August 2008 (PDT)