Simultaneous generating sets for flags
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916613115084800 |
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| author | Glaudo, Federico Kravitz, Noah Lowen, Chayim |
| author_facet | Glaudo, Federico Kravitz, Noah Lowen, Chayim |
| contents | We prove that any triple of complete flags in $\mathbb R^d$ admits a common generating set of size $\lfloor 5d/3\rfloor$ and that this bound is sharp. This result extends the classical linear-algebraic fact -- a consequence of the Bruhat decomposition of $\text{GL}_d(\mathbb R)$ -- that any pair of complete flags in $\mathbb R^d$ admits a common generating set of size $d$. We also deduce an analogue for $m$-tuples of flags with $m>3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_09530 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simultaneous generating sets for flags Glaudo, Federico Kravitz, Noah Lowen, Chayim Combinatorics Algebraic Geometry We prove that any triple of complete flags in $\mathbb R^d$ admits a common generating set of size $\lfloor 5d/3\rfloor$ and that this bound is sharp. This result extends the classical linear-algebraic fact -- a consequence of the Bruhat decomposition of $\text{GL}_d(\mathbb R)$ -- that any pair of complete flags in $\mathbb R^d$ admits a common generating set of size $d$. We also deduce an analogue for $m$-tuples of flags with $m>3$. |
| title | Simultaneous generating sets for flags |
| topic | Combinatorics Algebraic Geometry |
| url | https://arxiv.org/abs/2502.09530 |