P- and Q-Polynomial Association Schemes and Their Antipodal P-Polynomial Covers
نویسندگان
چکیده
منابع مشابه
Some algebra related to P- and Q-polynomial association schemes
Inspired by the theory of P -and Q-polynomial association schemes we consider the following situation in linear algebra. Let F denote a field, and let V denote a vector space over F with finite positive dimension. We consider a pair of linear transformations A : V → V and A : V → V satisfying the following four conditions. (i) A and A are both diagonalizable on V . (ii) There exists an ordering...
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If a nonsymmetric P-polynomial association scheme, or equivalently. a distanceregular digraph, has diameter d and girth g. then d = g or d = g 1, by Damerell’s theorem. The dual of this theorem was proved by Leonard. In this paper, we prove that the diameter of a nonsymmetric Pand Q-polynomial association scheme is one less than its girth and its cogirth. We also give a structure theorem for a ...
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It is well known that imprimitive P -polynomial association schemes X = (X, {Ri}0≤i≤d) with k1 > 2 are either bipartite or antipodal, i.e., intersection numbers satisfy either ai = 0 for all i, or bi = cd−i for all i 6= [d/2]. In this paper, we show that imprimitiveQ-polynomial association schemesX = (X, {Ri}0≤i≤d) with d > 6 and k∗ 1 > 2 are either dual bipartite or dual antipodal, i.e., dual ...
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It is well known that an association scheme X = (X, {Ri}0≤i≤d) with k1 > 2 has at most two P polynomial structures. The parametrical condition for an association scheme to have twoP -polynomial structures is also known. In this paper, we give a similar result for Q-polynomial association schemes. In fact, if d > 5, then we obtain exactly the same parametrical conditions for the dual intersectio...
متن کاملNew families of Q-polynomial association schemes
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 1993
ISSN: 0195-6698
DOI: 10.1006/eujc.1993.1039