Computing the Dimension of a Bipartition Matrix
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...
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| Zusammenfassung: | 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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| DOI: | 10.48550/arxiv.2111.05799 |