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Mathematical foundations of social anthropology by Paul A. Ballonoff

By Paul A. Ballonoff

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Q such that q eG is an offspring of q eG , q is a _ * (i-D (m) . (m+1) . (n) . (m) t parent of q , . . q is a parent of q , and ρ = q and q = q . qe(3. , If there exists a descent chain from q to p, then q is an ancestor of p, and ρ is a descendant of q. Note that if q is a parent of p, then q is also an ancestor of p; if ρ is an offspring of q, then ρ is also a descendant of q. Note also that for a pair of generations (G, G') with configurations (C, C/) and a descent map d:B' •+· M, if d(a) = M, then there exist, for each pea, two distinct elements of q M, each of which is an ancestor of p.

H + 2 ( I P (4,4) (t-2) Essentially, everything depends on the value of h, and on the initial β for the initial population(s). "regular" behavior. ) as δ > 3, depending on initial R, and dependent on the initial inbreeding of the initial pair, and on the "age structure" p^, ρ^ of breeding pairs after that. Notice, we do not have recursion in the proportions p.. or dependence of ρ 13 (t) other than for the same time period t, because we assume no on any values of relationship (independence) if fertility and matrix type by "age class", providing the class exists at all in a particular time period t.

D ^(n) :B „(n+1). figurations . . (n) , . " Note that under certain circumstances, the existence of a finite sequence permits construction of an infinite sequence of generations. For this reason, "sequence of generations" will mean "infinite sequence of generations" unless otherwise stated. A theorem on cyclic sequence construction is presented later. Notation is developed for displaying these pairs (G,G') in a graphic manner. f" to Show that the individual ρ represented by the dot is either pef or pem, respectively.

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