Computing the Dimension of a Bipartition Matrix
Combinatorics
2025-01-16 v6 Algebraic Topology
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).
Keywords
Cite
@article{arxiv.2111.05799,
title = {Computing the Dimension of a Bipartition Matrix},
author = {Dawson Freeman and Ronald Umble},
journal= {arXiv preprint arXiv:2111.05799},
year = {2025}
}
Comments
25 pages, 3 figures, typos corrected, edited for clarity