Partition is also an old name for types of compositions in several parts; there is no fixed meaning, and in several cases the term was reportedly interchanged with various other terms. A cross-partition is, "a two-dimensional configuration of pitch classes whose columns are realized as chords, and whose rows are differentiated from one another by registral, timbral, or other means." This allows, ""slot-machine" transformations that reorder the vertical trichords but keep the pitch classes in their columns." A mosaic is, "a partition that divides the aggregate into segments of equal size," according to Martino (1961). "Kurth 1992 and Mead 1988 use "mosaic" and "mosaic class" in the way that I use "partition" and "mosaic"," are used here. However later, he says that, "the DS determines the number of distinct partitions in a "mosaic", which is the set of partitions related by transposition and inversion." The first useful characteristic of a partition, an inventory is the set classes produced by the union of the constituent pitch class sets of a partition. For trichords and hexachords combined see Alegant 1993, Babbitt 1955, Dubiel 1990, Mead 1994, Morris and Alegant 1988, Morris 1987, and Rouse 1985; cited in. The second useful characteristic of a partition, the degree of symmetry (DS), "specifies the number of operations that preserve the unordered pcsets of a partition; it tells the extent to which that partition's pitch-class sets map into (or onto) each other under transposition or inversion."