Related papers: Choice functions on posets
The unit selection problem is to identify a group of individuals who are most likely to exhibit a desired mode of behavior, for example, selecting individuals who would respond one way if incentivized and a different way if not. The unit…
We introduce A-ranked preferential structures and combine them with an accessibility relation. This framework allows us to formalize contrary to duty obligations. Representation results are proved.
In this paper we introduce and study the poset of equivalence classes of subgroups of a finite group $G$, induced by the isomorphism relation. This contains the well-known lattice of solitary subgroups of $G$. We prove that in several…
A causal set is a countably infinite poset in which every element is above finitely many others; causal sets are exactly the posets that have a linear extension with the order-type of the natural numbers -- we call such a linear extension a…
This article examines differentiability properties of the value function of positioning choice problems, a class of optimisation problems in finite-dimensional Euclidean spaces. We show that positioning choice problems' value function is…
The paper is organized as a self-contained literate Haskell program that implements elements of an executable finite set theory with focus on combinatorial generation and arithmetic encodings. The code, tested under GHC 6.6.1, is available…
We consider Markov chains on partially ordered sets that generalize the success-runs and remaining life chains in reliability theory. We find conditions for recurrence and transience and give simple expressions for the invariant…
A poset is representable if it can be embedded in a field of sets in such a way that existing finite meets and joins become intersections and unions respectively (we say finite meets and joins are preserved). More generally, for cardinals…
For certain weak versions of the Axiom of Choice (most notably, the Boolean Prime Ideal theorem), we obtain equivalent formulations in terms of partial orders, and filter-like objects within them intersecting certain dense sets or…
We discuss the connections between the failure of the axiom of choice in set theory, and certain model-theoretic structures with enough symmetry.
A chain poset, by definition, consists of chains of ordered elements in a poset. We study the chain posets associated to two posets: the Boolean algebra and the poset of isotropic flags. We prove that, in both cases, the chain posets…
We lay down the foundations of a theory of parametrised functor calculus, generalising parts of the functor calculus of Goodwillie. We introduce the notion of excisable posets and develop a theory of excisive approximations in this context.…
A quasi-hereditary algebra is an Artin algebra together with a partial order on its set of isomorphism classes of simple modules which satisfies certain conditions. In this article we investigate all the possible choices that yield to…
We give a necessary and sufficient condition ensuring that any function which is separately Lipschitz on two fixed compact sets is Lipschitz on their union.
Motivated by applications for set containment problems, we consider the following fundamental problem: can we design set-to-vector functions so that the natural partial order on sets is preserved, namely $S\subseteq T \text{ if and only if…
Classical problems of sorting and searching assume an underlying linear ordering of the objects being compared. In this paper, we study a more general setting, in which some pairs of objects are incomparable. This generalization is relevant…
In this paper, we show that the presence of the Archimedean and the mixture-continuity properties of a binary relation, both empirically non-falsifiable in principle, foreclose the possibility of consistency (transitivity) without…
We consider a school choice matching model where the priorities for schools are represented by binary relations that may not be weak order. We focus on the (total order) extensions of the binary relations. We introduce a class of algorithms…
We present a unified framework to study threshold functions for the existence of solutions to linear systems of equations in random sets which includes arithmetic progressions, sum-free sets, $B_{h}[g]$-sets and Hilbert cubes. In…
We establish an equivalence between two seemingly different theories: one is the traditional axiomatisation of incomplete preferences on horse lotteries based on the mixture independence axiom; the other is the theory of desirable gambles…