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A generalization of pairwise intersecting Minkowski arrangement of centrallysymmetric convex bodies is the pairwise intersecting Minkowski arrangement oforder $\mu$. Here, the homothetic copies of a centrally symmetric convex bodyare so that none of their interiors intersect the $\mu$-kernel of any other. Wegive general upper and lower bounds on the cardinality of such arrangements,and study two special cases: For $d$-dimensional translates in classicalpairwise intersecting Minkowski arrangement we prove that the sharp upper boundis $3^d$. For $\mu=1$ the general version yields to another known problem: TheBezdek-Pach Conjecture asserts that the maximum number of pairwise touchingpositive homothetic copies of a convex body in $\mathbb{R}^d$ is $2^d$. Weverify the conjecture on the plane, that is, when $d=2$. Indeed, we show thatthe number in question is four for any planar convex body.

Bounds on Convex Bodies in Pairwise Intersecting Minkowski Arrangement of Order $\mu$