New families of Q-polynomial association schemes
نویسندگان
چکیده
منابع مشابه
New families of Q-polynomial association schemes
In this paper, we construct the first known infinite family of primitive Qpolynomial schemes which are not generated by distance-regular graphs. To construct these examples, we introduce the notion of a relative hemisystem of a generalized quadrangle with respect to a subquadrangle.
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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 was shown that linked systems of symmetric designs with a1 = 0 and mutually unbiased bases (MUBs) are triply regular association schemes. In this paper, we characterize triple regularity of linked systems of symmetric designs by its Krein number. And we prove that a maximal set of MUBs carries a quadruply regular association scheme and characterize the quadruple regularity of MUBs by its par...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2011
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2010.08.001