Computing the Dimension of a Bipartition Matrix
Abstract
The dimension of a bipartition matrix (BPM) is the sum of the dimensions of its indecomposable factors. The dimension of an indecomposable BPM is the sum of its row, column, and entry dimensions. To compute these dimensions, we apply four routines of independent interest: (1) Factor a bipartition as a product of indecomposables; (2) recover a bipartition from its indecomposable factorization; (3) factor a BPM as a product of indecomposables; and (4) compute the "transpose-rotation" (the column dimension of a BPM is the row dimension of its transpose-rotation).
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