Open AccessOn 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/the 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.