
handle: 11365/17507
In this interesting paper, the authors introduce the notion of a ``scattered set of points'' of a dual polar space as a set \(X\) of points such that every point of the dual polar space is at maximal distance from some point of \(X\). A minimal scattered set is one with the property that, if one removes any point from it, what remains is not a scattered set anymore. The maximum size of a minimal scattered set is called the scattered rank. The main results of the paper under review state that (1) every dual polar space of diameter \(n\) admits a minimal scattered set of size \(2^n\), and (2) if a dual polar space \(\Delta\) admits a polarized lax embedding in some projective space of dimension \(r-1\), then \(r\) is not smaller than the scattered rank of \(\Delta\).
Polar geometry, symplectic spaces, orthogonal spaces, embedding, Buildings and the geometry of diagrams, polarized embedding, Computational Theory and Mathematics, Geometry and Topology, dual polar spaces, 510, near polygons, Theoretical Computer Science
Polar geometry, symplectic spaces, orthogonal spaces, embedding, Buildings and the geometry of diagrams, polarized embedding, Computational Theory and Mathematics, Geometry and Topology, dual polar spaces, 510, near polygons, Theoretical Computer Science
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