Size-121 (= 11²) non-right-cancellative magma, all elements idempotent, satisfies eq255. Decomposes as a fiber-bundle-like structure: F_11(10,2) base × F_11(4,8) fiber. The 121 elements partition into 11 fibers of 11 elements (an F_11-quotient congruence), and EVERY fiber is itself an F_11(4,8) sub-magma. In addition, there is exactly one extra 11-element sub-magma — a transversal that hits each fiber in exactly one element — and this transversal is isomorphic to F_11(10,2) (matching the base operation). The 12 size-11 sub-magmas (11 fibers + 1 transversal) form an AG(2,11)-pencil-like configuration. The magma is left-cancellative but not right-cancellative, distinguishing it from the direct product F_11(10,2) × F_11(4,8) (which would be both LC and RC). Each pair of distinct elements is contained in exactly one of the 12 size-11 sub-magmas (covering 660 = 12·C(11,2) of the 7260 = C(121,2) total pairs); pairs across two distinct fibers and not on the transversal lie in no sub-magma.
dwrensha · 2026-04-29 15:40:00