On the quasi polynomiality of extremal homology of configuration spaces

Consider the unordered configuration spaces of manifolds. Knudsen, Miller and Tosteson proved that the extremal homology groups of configuration spaces of manifold are eventually quasi polynomials. In this paper, we give the precise degree of top non-trivial quasi polynomials. This shows that the upper bound of Knudsen, Miller and Tosteson for the degree of quasi polynomials is sharp for every manifold.