Arrangement

In "Hyakunin Isshu", each of the "100" poets gives "1" poem, which denotes the corresponding poet as an "element" of the set. However, if those 100 poets are perceived as "parts" instead, with all the possible combinations exhausted, the number of those parts will explode up to 2^100 (2 to the 100th power). The "101" poems in "Hyakunin Shuuka", recently discovered and considered to be the prototype of "Hyakunin Isshu", with political sensitivities suggested such as excluding the poems of the two emperors, Go-Toba-in (the author of 99th poem in “Hyakunin Isshu”) and Juntoku-in (100th), seem to fix such an explosion.

2^100 ≡ 1 (mod 101)

Thus, Fermat's Little Theorem turns the diverging parts (2^100) into a cycle that recurs to "1" as seen in the sequence below, which would be the projection of the hyper-structure onto the original structure.

However, the symmetry of "Hyakunin Isshu", in which the two emperors are located at the beginning and the other two at the end of the book, is possible to be preserved by reversing the second half of the above sequence (100 - 51), as shown below. This order, which, so to speak, seems to be in between structure and hyper-structure, has been used for the composition “Comments for Hyakunin Isshu” as if the 100 poems were arranged without being arranged.