Inconsistency of special cases of pairwise comparisons matrices

All studied special cases of PC matrices are Toeplitz matrices with only three different entries 1, x, and 1/x. A circulant matrix has been used for pairwise comparisons to analyze inconsistency. Although this class of PC matrices may be perceived as restricted, it is general enough to cover all values of the eigenvalue-based inconsistency index from the lowest to the highest. Both exact mathematical expressions and estimations, where the exact expression was impossible to find, are provided.