Generalized degree-power star conjecture for t-intersecting families

Let $1\leq t\leq k$, $1\leq r\leq k-1$, and let $p\geq2$ be real. Suppose that

$$n\geq(t+1)(k-t+1).$$

If $\mathcal F\subseteq\binom{[n]}k$ is $t$-intersecting, then, for every $T\in\binom{[n]}t$, define $\ell_{r,p}(\mathcal F)$ as the degree-power quantity used in the paper. Generalized degree-power star conjecture.

$$\ell_{r,p}(\mathcal F)\leq\ell_{r,p}(\mathcal S_T).$$

This conjecture simultaneously extends the cases $r=k-1$ and $t=1$, established in the paper. Its parameter range is the sharp classical star range associated with Wilson's theorem and the Ahlswede--Khachatrian complete intersection theorem; the restriction $p\geq2$ is essential, as the paper gives a counterexample for $1<p<2$.