We prove that the parameter $x$ of a tight set $\mathcal{ T}$ of a hyperbolic quadric $\mathsf{ Q}^+(2n+1,q)$ of an odd rank $n+1$ satisfies ${ x\choose 2}+w(w-x)\equiv 0\mod q+1$, where $w$ is the number of points of $\mathcal{ T}$ in any generator of $\mathsf{ Q}^+(2n+1,q)$. As this modular equation should have an integer solution in $w$ if such a $\mathcal{ T}$ exists, this condition rules out roughly at least one half of all possible parameters $x$. It generalizes a previous result by the author and K. Metsch shown for tight sets of a hyperbolic quadric $\mathsf{ Q}^+(5,q)$ (also known as Cameron-Liebler line classes in $\mathrm{ PG}(3,q)$).
Categories: math.CO