On the Smallest Non-Trivial Tight Sets in Hermitian Polar Spaces | Zendy

Jan De Beule | Zendy; Klaus Metsch | Zendy

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On the Smallest Non-Trivial Tight Sets in Hermitian Polar Spaces

Author(s) -

Jan De Beule,

Klaus Metsch

Publication year - 2017

Publication title -

the electronic journal of combinatorics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.703

H-Index - 52

eISSN - 1097-1440

pISSN - 1077-8926

DOI - 10.37236/6461

Subject(s) - disjoint sets , mathematics , hermitian matrix , combinatorics , polar , space (punctuation) , upper and lower bounds , hypergraph , disjoint union (topology) , discrete mathematics , physics , pure mathematics , mathematical analysis , quantum mechanics , computer science , operating system

We show that an $x$-tight set of the Hermitian polar spaces $\mathrm{H}(4,q^2)$ and $\mathrm{H}(6,q^2)$ respectively, is the union of $x$ disjoint generators of the polar space provided that $x$ is small compared to $q$. For $\mathrm{H}(4,q^2)$ we need the bound $x<q+1$ and we can show that this bound is sharp.

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