For positive integers and , consider a multiset of nonempty subsets such that there is unique partition these into partitions . We study the maximum possible size multiset. focus on regime show When for any this lower bound simplifies to we matching upper optimal up factor also compute exactly when

We prove that the family of measured dynamical systems which can be realised as uniquely ergodic minimal homeomorphisms on a given manifold (of dimension at least two) is stable under measured extension. As a corollary, any ergodic system with an irrational eigenvalue is isomorphic to a uniquely ergodic minimal homeomorphism on the two-torus. The proof uses the following improvement of Weiss re...

A range of research has explored the problem of generating referring expressions that uniquely identify a single entity from the shared context. But what about expressions that identify sets of entities? In this paper, I adapt recent semantic research on plural descriptions—using covers to abstract collective and distributive readings and using sets of assignments to represent dependencies amon...

Previous research reveals that individual differences in parental caregiving motives have implications (among both parents and nonparents) for a wide range of psychological outcomes. Here we report reanalyses of existing data sets to examine the extent to which these outcomes are uniquely predicted by two conceptually distinct factors underlying the parental caregiving motive: protection and nu...

Eccentric coloring is a new variation of coloring, where higher numbered colors can not be used as freely as lower numbered colors. In addition there is a correspondence between the eccentricity (max distance) of a vertex and the highest legal color for that vertex. In this note we investigate eccentric coloring of trees. We give the eccentric chromatic number or a bound on the eccentric chroma...