Related papers: How Expressive Are Friendly School Partitions?
We introduce a generalized cake-cutting problem in which we seek to divide multiple cakes so that two players may get their most-preferred piece selections: a choice of one piece from each cake, allowing for the possibility of linked…
Mass partition problems describe the partitions we can induce on a family of measures or finite sets of points in Euclidean spaces by dividing the ambient space into pieces. In this survey we describe recent progress in the area in addition…
The famous partition theorem of Euler states that partitions of $n$ into distinct parts are equinumerous with partitions of $n$ into odd parts. Another famous partition theorem due to MacMahon states that the number of partitions of $n$…
An $({\cal F},{\cal F}_d)$-partition of a graph is a vertex-partition into two sets $F$ and $F_d$ such that the graph induced by $F$ is a forest and the one induced by $F_d$ is a forest with maximum degree at most $d$. We prove that every…
In their study of physics beyond the first year of University -- termed upper-division in the US, many of students' primary learning opportunities come from working long, complex back-of-the-book style problems, and from trying to develop…
The fair division literature in economics considers how to divide resources between multiple agents such that the allocation is envy-free: each agent receives their favorite piece. Researchers have developed a variety of fair division…
E394 in the Enestrom index. Translated from the Latin original, "De partitione numerorum in partes tam numero quam specie datas" (1768). Euler finds a lot of recurrence formulas for the number of partitions of $N$ into $n$ parts from some…
A {\bf $\mathbf{k}$-majority coloring} of a digraph $D=(V,A)$ is a coloring of $V$ with $k$ colors so that each vertex $v\in V$ has at least as many out-neighbours of color different from its own color as it has out-neighbours with the same…
In multistage group testing, the tests within the same stage are considered nonadaptive, while those conducted across different stages are adaptive. Specifically, when the pools within the same stage are disjoint, meaning that the entire…
We consider the {\em vector partition problem}, where $n$ agents, each with a $d$-dimensional attribute vector, are to be partitioned into $p$ parts so as to minimize cost which is a given function on the sums of attribute vectors in each…
The theory of two-sided matching has been extensively developed and applied to many real-life application domains. As the theory has been applied to increasingly diverse types of environments, researchers and practitioners have encountered…
We study families of positive and completely positive maps acting on a bipartite system $\mathbb{C}^M\otimes \mathbb{C}^N$ (with $M\leq N$). The maps have a property that when applied to any state (of a given entanglement class) they result…
The lattice of partitions of a set and its d-divisible generalization have been much studied for their combinatorial, topological, and representation-theoretic properties. An ordered set partition is a set partition where the subsets are…
In higher education, data is collected that indicate the term(s) that a course is taken and when it is passed. Often, study plans propose a suggested course order to students. Study planners can adjust these based on detected deviations…
Biological and social scientists have long been interested in understanding how to reconcile individual and collective interests in iterated Prisoner's Dilemma. Many effective strategies have been proposed, and they are often categorized…
We describe a solution to the student-project allocation problem using simulated annealing. The problem involves assigning students to projects, where each student has ranked a fixed number of projects in order of preference. Each project…
Several countries successfully use centralized matching schemes for school or higher education assignment, or for entry-level labour markets. In this paper we explore the computational aspects of a possible similar scheme for assigning…
In this paper, we focus on families of bipartitions, i.e. set partitions consisting of at most two components. We say that a family of bipartitions is a separating family for a set $S$ if every two elements in $S$ can be separated by some…
We recall the notion of fractional enumeration and immediately focus on the fractional counting of integer partitions, where each partition gets credit equal to the reciprocal of the product of its parts. We raise two intriguing questions…
In this paper, we consider the asymptotic properties of hook numbers of partitions in restricted classes. More specifically, we compare the frequency with which partitions into odd parts and partitions into distinct parts have hook numbers…