Dimension-counting bounds for equi-isoclinic subspaces
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914170967949312 |
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| author | Iverson, Joseph W. O, Kaysie Rose |
| author_facet | Iverson, Joseph W. O, Kaysie Rose |
| contents | We make four contributions to the theory of optimal subspace packings and equi-isoclinic subspaces: (1) a new lower bound for block coherence, (2) an exact count of equi-isoclinic subspaces of even dimension $r$ in $\mathbb{R}^{2r+1}$ with parameter $α\neq \tfrac{1}{2}$, (3) a new upper bound for the number of $r$-dimensional equi-isoclinic subspaces in $\mathbb{R}^d$ or $\mathbb{C}^d$, and (4) a proof that when $d=2r$, a further refinement of this bound is attained for every $r$ in the complex case and every $r=2^k$ in the real case. For each of these contributions, the proof ultimately relies on a dimension count. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_20642 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dimension-counting bounds for equi-isoclinic subspaces Iverson, Joseph W. O, Kaysie Rose Information Theory Combinatorics Functional Analysis Metric Geometry We make four contributions to the theory of optimal subspace packings and equi-isoclinic subspaces: (1) a new lower bound for block coherence, (2) an exact count of equi-isoclinic subspaces of even dimension $r$ in $\mathbb{R}^{2r+1}$ with parameter $α\neq \tfrac{1}{2}$, (3) a new upper bound for the number of $r$-dimensional equi-isoclinic subspaces in $\mathbb{R}^d$ or $\mathbb{C}^d$, and (4) a proof that when $d=2r$, a further refinement of this bound is attained for every $r$ in the complex case and every $r=2^k$ in the real case. For each of these contributions, the proof ultimately relies on a dimension count. |
| title | Dimension-counting bounds for equi-isoclinic subspaces |
| topic | Information Theory Combinatorics Functional Analysis Metric Geometry |
| url | https://arxiv.org/abs/2511.20642 |