1,731 research outputs found
Implications of Pareto Efficiency for Two-Agent (Household) Choice
We study when two-member household choice behavior is compatible with Pareto optimality. We ask when an external observer of household choices, who does not know the individuals' preferences, can rationalize the choices as being Pareto-optimal. Our main contribution is to reduce the problem of rationalization to a graph-coloring problem. As a result, we obtain simple tests for Pareto optimal choice behavior. In addition to the tests, and using our graph-theoretic representation, we show that Pareto rationalization is equivalent to a system of quadratic equations being solvable
An Infinite self dual Ramsey theorem
In a recent paper \cite{So} S. Solecki proves a finite self dual Ramsey
theorem that in a natural way gives simultaneously the classical finite Ramsey
theorem \cite{Ra} and the Graham-Rothschild theorem \cite{Gr-Ro}. In this paper
we prove the corresponding infinite dimensional self dual theorem, giving
similarly as a consequence the infinite classical Ramsey theorem \cite{Ra} and
the Carlson-Simpson theorem \cite{Ca-Si}
Ramseyan ultrafilters
We investigate families of partitions of omega which are related to special
coideals, so-called happy families, and give a dual form of Ramsey ultrafilters
in terms of partitions. The combinatorial properties of these
partition-ultrafilters, which we call Ramseyan ultrafilters, are similar to
those of Ramsey ultrafilters. For example it will be shown that dual Mathias
forcing restricted to a Ramseyan ultrafilter has the same features as Mathias
forcing restricted to a Ramsey ultrafilter. Further we introduce an ordering on
the set of partition-filters and consider the dual form of some cardinal
characteristics of the continuum
Quantum invariants of 3-manifolds via link surgery presentations and non-semi-simple categories
In this paper we construct invariants of 3-manifolds "\`a la
Reshetikhin-Turaev" in the setting of non-semi-simple ribbon tensor categories.
We give concrete examples of such categories which lead to a family of
3-manifold invariants indexed by the integers. We prove this family of
invariants has several notable features, including: they can be computed via a
set of axioms, they distinguish homotopically equivalent manifolds that the
standard Reshetikhin-Turaev-Witten invariants do not, and they allow the
statement of a version of the Volume Conjecture and a proof of this conjecture
for an infinite class of links.Comment: 46 pages, 45 figures, new introduction, some misprints corrected and
an example detailed. An appendix added to correct a proo
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