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|In particular, it is shown that this is the case only if d = 2. It is noted that some of these algebras come from association schemes and some do not.|
|Clearly, for any choice of n + 1 distinct real numbers z z , we can find polynomials |
$,...,$, each of degree at most n, such that P = $k(z.) for 0 s i, k ^ n. Delsarte calls
a scheme P-polynomial if there is a choice of z z with z = 0 for which *. has ...
|Theorem 9. If N — P > M and k > 0, then an N x P polynomial M-variate matrix H(z|
) of degree at most k is generically Laurent polynomial left invertible. Proof. By
above remark, we know that if a polynomial matrix H (z) is Laurent polynomial left
|If a that degree is already in p, then it is or added in (true). } load (var p : |
polynomial); recycle (var p : polynomial); purge (var p : polynomial); all terms with
negligible coefficient } copy poly (p: polynomial) : polynomial; print (p: polynomial
); mult ...
|Theory and Practice : [proceedings of the NATO Advanced Study Institute on "|
Orthogonal Polynomials and Their Applications," ... Here we will mention non-
existence results for perfect codes and tight t-designs in known P- and Q -
|This book is written for specialists in numerical analysis and will also appeal to mathematicians in general.|
Ronald Cleveland Mullin, Gary L. Mullen - 1999 - Preview
|Then any (ps,d)-polynomial of Fq of the form X(X^P i)/d ~ a)d can not be obtained |
through the composition of (ps,d)-polynomials over ¥q. If it did decompose as (ps,
d)-polynomials then they would all have degree < ps and the only such ...
|Figure 6. A Hopf link with a different orientation from that of L_ in Figure 5. rection |
from the Hopf link which is illustrated as L_ in Figure 5. The P-polynomial of this
new Hopf link turns out to equal l_3m_1 + l_1m_1 — l'lm. The roles of l and l '1 ...
|However, the link polynomials do not distinguish every pair of knots or links. In |
fact, Kanenobu (1986) has shown that there are infinitely many knots with the
same P-polynomial. The following theorem will tell us how to conclude from the ...