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A circulant matrix is a square matrix where each row has the same elements as the previous row, cyclically rotated right by one element. It is a specific kind of a square Toeplitz matrix.

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Is this general form of Lovasz theta function of circulant graphs?

Computing Lovasz $\theta$ for circulant graphs can be reduced to linear programming; this is well-known, I think (already mentioned in A.Schrijver's 1979 paper "A comparison of the Delsarte and Lovasz …
Dima Pasechnik's user avatar