Consider the collection of all integer partitions, whose part sizes lie in a given set. Such a set is called monotone if the generating function has weakly increasing coefficients. The monotone subsets are classified, assuming an open conjecture.

Confluence of term rewriting systems (TRSs) is undecidable, even for flat TRSs [MOJ06] or length-two string rewrite systems [SW08]. Two decidable subclasses are known: right-linear and shallow TRSs by tree automata techniques [GT05] and terminating TRSs [KB70]. Most of sufficient conditions are for either terminating TRSs [KB70] (extended to TRSs with relative termination [HA11, KH12]) or leftl...

Assumptions on a likelihood function, including a local GlivenkoCantelli condition, imply the existence of M-estimators converging to an Mfunctional. Scatter matrix-valued estimators, defined on all empirical measures on R for d ≥ 2, and equivariant under all, including singular, affine transformations, are shown to be constants times the sample covariance matrix. So, if weakly continuous, they...