Computing the Dimension of a Bipartition Matrix

We present a computer program that computes the dimension of a bipartition matrix, which has three independent components: the row dimension, the column dimension, and the entry dimension. Each component is defined recursively and as such is well-suited for machine computation. The program applies several routines of independent interest, namely, a routine that factors a bipartition as a formal product of indecomposable bipartiition matrices; its inverse, which recovers the bipartition; a routine that factors a general bipartition matrix as a formal product of indecomposables; and a routine that calculates its "transpose-rotation." The column dimension of a bipartition matrix is the row dimension of its transpose-rotation.