Rainbow Tower Rainbow Tower The Rainbow Tower is a tower located at the Rainbow Plaza Canada–US border station of the Rainbow Bridge in Niagara Falls, Ontario, Canada. Construction on the tower was completed in 1947. The tower, part of the Canadian plaza of the bridge, was designed by Canadian architect William Lyon Somerville. The Rainbow Tower houses a carillon—a musical instrument consisting of a baton keyboard that controls a series of bells. The Rainbow Carillon is sounded three times a day, 365 days a year. It features 55 bells with a total weight of over 43 tons. The instrument is controlled via
Partition of a set "coarser" than "α"—if every element of "α" is a subset of some element of "ρ". Informally, this means that "α" is a further fragmentation of "ρ". In that case, it is written that "α" ≤ "ρ". This "finer-than" relation on the set of partitions of "X" is a partial order (so the notation "≤" is appropriate). Each set of elements has a least upper bound and a greatest lower bound, so that it forms a lattice, and more specifically (for partitions of a finite set) it is a geometric lattice. The "partition lattice" of a 4-element set has 15 elements