Suppose there exist an n-tuple
of strategies [mathematical expression not reproducible] and a trajectory [mathematical expression not reproducible] satisfying (2).
Let J be a distinct-integer N-tuple
([j.sub.1], ..., [j.sub.N]), and let [mathematical expression not reproducible] be the system (11.5), where [[??].sub.p,jl] are the jl-th p-adic w-s motions (11.2), for all l = 1, ..., N.
Indeed the similar conclusions could be obtained for the n-tuple
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], we leave the proof for the readers.
An m-repeated low-density burst of length b(fixed) with weight w or less is an n-tuple
whose only non-zero components are confined to m distinct sets of b consecutive positions, the first component of each set is non-zero where each set can have at the most w non-zero components (w [less than or equal to] b), and the number of its starting positions in an n-tuple
is among the first n - mb + 1 positions.
of real n-tuples
or, in 'frequency domain', by component-wise multiplication of (complex) n-tuples
([a.sub.1], [a.sub.2], ...,[a.sub.n]) is the identity n-tuple
, if [a.sub.k] = +, for 1 [less than or equal to] k [less than or equal to] n, otherwise it is a non-identity n-tuple
Note that the ambiguity in choosing an n-tuple
for the weight [lambda] amounts to an integral translation of GT([lambda]), and hence does not affect its number of integral points.
We write m = [summation over (n/j=1)] [m.sub.j][e.sub.j], where [e.sub.j] is an n-tuple
with 1 in the jth position and 0's elsewhere, and we define 0 = (0, ..., 0).
Next, enumerate the elements of S and then, in the usual way, identify each subset of S with an n-tuple
of 0's and l's.
A voting pattern is an assignment of a strategy to each participant, in the form of an n-tuple
A CSP is a triple P = (X, D, C), where X is an n-tuple
of variables X = ([x.sub.1], [x.sub.2], ..., [x.sub.n]), D is a corresponding n-tuple
of domains D = ([D.sub.1], [D.sub.2], ..., [D.sub.n]) such that [x.sub.i] [member of] [D.sub.i], and C is a f-tuple of constraints C = ([C.sub.1], [C.sub.2],...., [C.sub.t]).
([a.sub.1], [a.sub.2], ..., [a.sub.n]) is symmetric, if [a.sub.k] = [a.sub.n-k+1], 1 [less than or equal to] k [less than or equal to] n.