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We study the problem of factorization for residues of generalized biadjointscalar scattering amplitudes $m^{(k)}_n$, introduced by Cachazo, Early, Guevaraand Mizera (CEGM), involving multi-dimensional residues which factorizegenerically into $k$-ary products of lower-point generalized biadjointamplitudes of the same type $m^{(k)}_{n_1}\cdots m^{(k)}_{n_k}$, where$n_1+\cdots +n_k = n+k(k-1)$, noting that smaller numbers of factors arise asspecial cases. Such behavior is governed geometrically by regular matroidsubdivisions of hypersimplices and cones in the positive tropical Grassmannian,and combinatorially by collections of compatible decorated ordered setpartitions, considered modulo cyclic rotation. We make a proposal forconditions under which this happens and we develop $k=3,4$ in detail. Weconclude briefly to propose a novel formula to construct coarsest regularmatroid subdivisions of all hypersimplices $\Delta_{k,n}$ and rays of thepositive tropical Grassmannian, which should be of independent interest.

Factorization for Generalized Biadjoint Scalar Amplitudes via Matroid Subdivisions