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- W1991088029 abstract "The association schemes of the dual polar spaces of type B d (q) and C d ( q ) have the same parameters, but they are isomorphic if and only if q is even. Let Y = ( X , { R i } 0 ⩽ i ⩽ d ) be either of these schemes. Put R ^ 0 = R 0 , R ^ 1 = R 2 i − 1 ∪ R 2 i for 1 ⩽ i ⩽ d ^ , where d ^ = [ ( d + 1 ) / 2 ] and it is assumed that R d+1 =∅. Then Y ^ = ( X , { R ^ i } 0 ⩽ i ⩽ d ^ ) is a ( P and Q )-polynomial association scheme. Moreover, B ^ d ( q ) is isomorphic to the halved scheme of the dual polar space scheme of type D d +1 ( q ), while C ^ d ( q ) is new for odd q and d ⩾ 3 and the distance-regular graph related to this scheme is not distance-transitive." @default.
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- W1991088029 date "1989-07-01" @default.
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- W1991088029 title "On a New Family of (P and Q)-polynomial Schemes" @default.
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- W1991088029 doi "https://doi.org/10.1016/s0195-6698(89)80006-x" @default.
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