Intersection patterns of set systems on manifolds with slowly growing homological shatter functions

Sergey Avvakumov, Marguerite Bin, Xavier Goaoc

A theorem of Matoušek asserts that for any $k\ge 2$, any set system whose shatter function is $o(n^k)$ enjoys a fractional Helly theorem of order $k$: in the $k$-wise intersection…