Exact inducibility and statistics functions beyond asymptotic constants

Establish exact values of the inducibility or statistics functions for sufficiently large dimensions or sizes in cases where the paper determines only their asymptotic constants, including by determining whether the available flag-algebra certificates can yield such exact formulas.

Background

The main results determine several asymptotic inducibility and statistics constants, but exact finite-dimensional functions are obtained only for the configuration $W_{12}$. The authors discuss whether flag-algebra certificates might be strengthened to prove exact extremal functions for all sufficiently large $n$. They note that existing approaches based on stability are complicated by the flexibility of hypercube configurations and explicitly identify the usefulness of local stability as unresolved.