Related papers: Social welfare relations and irregular sets
We study the question of dividing a collection of indivisible goods amongst a set of agents. The main objective of research in the area is to achieve one of two goals: fairness or efficiency. On the fairness side, envy-freeness is the…
We say that binary relation E on a space X is a clopen graph on X iff E is symmetric and irreflexive and clopen relative to X x X minus its diagonal. Equivalently for distinct x, y in X there are open sets U,V with (x,y) in U x V and either…
Sequential allocation is a simple and attractive mechanism for the allocation of indivisible goods. Agents take turns, according to a policy, to pick items. Sequential allocation is guaranteed to return an allocation which is efficient but…
The uneven distribution of wealth and individual economic capacities are among the main forces which shape modern societies and arguably bias the emerging social structures. However, the study of correlations between the social network and…
Integral relations with the Cauchy kernel on a semi-axis for the Laguerre polynomials, the confluent hypergeometric function, and the cylindrical functions are derived. A part of these formulas is obtained by exploiting some properties of…
Sets of desirable gambles constitute a quite general type of uncertainty model with an interesting geometrical interpretation. We give a general discussion of such models and their rationality criteria. We study exchangeability assessments…
A new mechanism leading to scale-free networks is proposed in this letter. It is shown that in many cases of interest, the connectivity power-law behavior is neither related to dynamical properties nor to preferential attachment. Instead,…
We prove that if $G$ is a totally bounded abelian group \st\ its dual group $\widehat{G}_p$ equipped with the finite-open topology is a Baire group, then every compact subset of $G$ must be finite. This solves an open question by Chasco,…
Network data appear in a number of applications, such as online social networks and biological networks, and there is growing interest in both developing models for networks as well as studying the properties of such data. Since individual…
The Constraint Satisfaction Problem (CSP) and its counting counterpart appears under different guises in many areas of mathematics, computer science, and elsewhere. Its structural and algorithmic properties have demonstrated to play a…
We continue the study initiated in [F. Albiac and P. Wojtaszczyk, Characterization of $1$-greedy bases, J. Approx. Theory 138 (2006), no. 1, 65-86] of properties related to greedy bases in the case when the constants involved are sharp,…
For a projective variety $X$ defined over a non-Archimedean complete non-trivially valued field $k$, and a semipositive metrized line bundle $(L, \phi)$ over it, we establish a metric extension result for sections of $L^{\otimes n}$ from a…
The paper provides important insights into understanding the factors that influence tie strength in social networks. Using local network measures that take into account asymmetry of social interactions we show that the observed tie strength…
Szemeredi's Regularity Lemma is a very useful tool of extremal combinatorics. Recently, several refinements of this seminal result were obtained for special, more structured classes of graphs. We survey these results in their rich…
The interpretation of the violation of Bell-Clauser-Horne inequalities is revisited, in relation with the notion of extension of QM predictions to unmeasurable correlations. Such extensions are compatible with QM predictions in many cases,…
Building on established literature and recent developments in the graph-theoretic characterisation of its CPM category, we provide a treatment of pure state and mixed state quantum mechanics in the category fRel of finite sets and…
In this paper we give a characterisation of real closure * of regular rings, which is quite similar to the characterisation of real closure * of Baer regular rings seen in [4]. We also characterize Baer-ness of regular rings using near-open…
It is shown that a finitely generated branch group has Serre's property (FA) if and only if it does not surject onto the infinite cyclic group or the infinite dihedral group. An example of a finitely generated self-similar branch group…
In the additive topological group $(\mathbb{R},+)$ of real numbers, we construct families of sets for which elements are not measurable in the Lebesgue sense. The constructed families have algebraic structures of being semigroups (i.e.,…
Accidental symmetries in effective field theories can be established by computing and comparing Hilbert series. This invites us to study them with the tools of invariant theory. Applying this technology, we spotlight three classes of…