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Minimal scattered sets and polarized embeddings of dual polar spaces

Authors: DE BRUYN B.; PASINI A.;

Minimal scattered sets and polarized embeddings of dual polar spaces

Abstract

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 \(\Delta\).

Country
Italy
Related Organizations
Keywords

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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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
9
Average
Top 10%
Top 10%
hybrid