Gauss-type formulas for link map invariants

We find that Koschorke's $\beta$-invariant and the triple $\mu$-invariant of link maps in the critical dimension can be computed as degrees of certain maps of configuration spaces - just like the linking number. Both formulas admit geometric interpretations in terms of Vassiliev's ornaments via new operations akin to the Jin suspension, and both were unexpected for the author, because the only known direct ways to extract $\mu$ and $\beta$ from invariants of maps between configuration spaces involved some homotopy theory (Whitehead products and the stable Hopf invariant, respectively).