Simultaneous generating sets for flags

2025/02/13 by Federico Glaudo, Glaudo, Federico, Noah Kravitz +3
Computer Science · Engineering · #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Robotic Path Planning Algorithms #Vehicle Routing Optimization Methods

paper · pdf · doi:10.48550/arxiv.2502.09530

openalex publication_date 2025/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 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.

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