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The algorithm calculates coeficients of low-degree summands up to the given fixed degree k.
The repeatedly occurring summands strongly support the idea of a self-similar, fractal structure as Muller already claimed in reference [2].
q]-connection on a left U-module E, [pi] is the projection on the first summand in the direct sum M [direct sum] N, and [pi]([omega] [[cross product].
Therefore, linear parameters v, a, a' of the stationary rotation are described by the first summands in the right part of the formulas (13)-(15).
In order to find an estimate for the remaining summand [theta](t), we use (2.
v]], with one summand per "checker game" (a sequence of compatible checkerboards).
and rewrite the second summand as a projection in terms of the Euclidean scalar product (,),
The first summand in (5) is just the weighted sum of individual utility levels that have to be maximized subject to three constraints: First, the final wealth of each individual must not decrease if the aggregate wealth increases.
Accordingly, let us say that a matroid M over R is full-rank if no nontrivial projective module is a direct summand of M(E).
For i > 0, by induction the second summand on the right-hand side of (6) vanish.
Thus, it is sufficient to verify the inequality on each summand.
Note that while the statement of the corollary seems to have negative powers of q, in fact, each summand is a polynomial in q.