Related papers: The fair soup division and approximating numbers
Recently, Landau, Reid and Yershov provided a novel solution to the problem of redistricting. Instead of trying to ensure fairness by restricting the shape of the possible maps or by assigning the power to draw the map to nonbiased…
The paper considers fair allocation of resources that are already allocated in an unfair way. This setting requires a careful balance between the fairness considerations and the rights of the present owners. The paper presents re-division…
In this note, we present a substantial improvement on the computational complexity of the Erd\"{o}s-Szekeres partitioning problem and review recent works on dynamic \textsf{LIS}.
In this paper, we consider the fractional sum of the divisor functions. We can improve previous results considered by Bordell\'{e}s \cite{Bo} and Liu-Wu-Yang \cite{LWY}.
We overview results on the topic of Poisson approximation that are missed in existing surveys. The topic of Poisson approximation to the distribution of a sum of integer-valued random variables is presented as well. We do not restrict…
We give a counterexample to a recently conjectured variant of the Penrose inequality.
Two possibly unfair $n$-sided dice, both labelled $1, 2, \ldots, n$, are rolled, and the sum is recorded. How should the dice's sides be weighted so that the resulting sum is closest to the uniform distribution on $2, 3, \ldots, 2n$? We…
How to handle division in systems that compute with logical formulas involving what would otherwise be polynomial constraints over the real numbers is a surprisingly difficult question. This paper argues that existing approaches from both…
Fair division is a significant, long-standing problem and is closely related to social and economic justice. The conventional division methods such as cut-and-choose are hardly applicable to realworld problems because of their complexity…
The classic cake-cutting problem provides a model for addressing fair and efficient allocation of a divisible, heterogeneous resource (metaphorically, the cake) among agents with distinct preferences. Focusing on a standard formulation of…
The Lie algebras over the algebra of dual numbers are introduced and investigated.
Fair division is the problem of dividing one or several goods amongst two or more agents in a way that satisfies a suitable fairness criterion. These Notes provide a succinct introduction to the field. We cover three main topics. First, we…
We study the inverse problem of recovering the order and the diffusion coefficient of an elliptic fractional partial differential equation from a finite number of noisy observations of the solution. We work in a Bayesian framework and show…
We revisit two NP-hard geometric partitioning problems - convex decomposition and surface approximation. Building on recent developments in geometric separators, we present quasi-polynomial time algorithms for these problems with improved…
We survey a variety of results about partially isometric matrices. We focus primarily on results that are distinctly finite-dimensional. For example, we cover a recent solution to the similarity problem for partial isometries. We also…
We obtain a small improvement of Gallagher's larger sieve and we extend it to higher dimensions. We also obtain two interesting upper bounds for the number of solutions to polynomial congruences.
We present a new numerical tool to solve partial differential equations involving Caputo derivatives of fractional variable order. Three Caputo-type fractional operators are considered, and for each one of them an approximation formula is…
The problem of root mean square approximation of a square integrable function by finite linear combinations of exponential functions is considered. It is subdivided into linear and nonlinear parts. The linear approximation problem is…
We investigate the partitioning of partial orders into a minimal number of heapable subsets. We prove a characterization result reminiscent of the proof of Dilworth's theorem, which yields as a byproduct a flow-based algorithm for computing…
The Simes inequality has received considerable attention recently because of its close connection to some important multiple hypothesis testing procedures. We revisit in this article an old result on this inequality to clarify and…