Related papers: At most $3.55^n$ stable matchings
It is well-known that every maximal planar graph has a matching of size at least $\tfrac{n+8}{3}$ if $n\geq 14$. In this paper, we investigate similar matching-bounds for maximal \emph{1-planar} graphs, i.e., graphs that can be drawn such…
Feldman and Karlin conjectured that the number of isolated fixed points for deterministic models of viability selection and recombination among n possible haplotypes has an upper bound of 2^n - 1. Here a proof is provided. The upper bound…
In the context of mining for frequent patterns using the standard levelwise algorithm, the following question arises: given the current level and the current set of frequent patterns, what is the maximal number of candidate patterns that…
Consider finite sequences $X_{[1,n]}=X_1\dots X_n$ and $Y_{[1,n]}=Y_1\dots Y_n$ of length $n$, consisting of i.i.d.\ samples of random letters from a finite alphabet, and let $S$ and $T$ be chosen i.i.d.\ randomly from the unit ball in the…
This paper considers two-sided matching with budget constraints where one side (firm or hospital) can make monetary transfers (offer wages) to the other (worker or doctor). In a standard model, while multiple doctors can be matched to a…
What is the maximum number of intersections of the boundaries of a simple $m$-gon and a simple $n$-gon, assuming general position? This is a basic question in combinatorial geometry, and the answer is easy if at least one of $m$ and $n$ is…
We study the minimum number of constraints needed to formulate random instances of the maximum stable set problem via linear programs (LPs), in two distinct models. In the uniform model, the constraints of the LP are not allowed to depend…
We give an upper bound on the number of perfect matchings in an undirected simple graph $G$ with an even number of vertices, in terms of the degrees of all the vertices in $G$. This bound is sharp if $G$ is a union of complete bipartite…
We solve two long-standing open problems on word equations. Firstly, we prove that a one-variable word equation with constants has either at most three or an infinite number of solutions. The existence of such a bound had been conjectured,…
We introduce the {\sc classified stable matching} problem, a problem motivated by academic hiring. Suppose that a number of institutes are hiring faculty members from a pool of applicants. Both institutes and applicants have preferences…
Complementation of finite automata on infinite words is not only a fundamental problem in automata theory, but also serves as a cornerstone for solving numerous decision problems in mathematical logic, model-checking, program analysis and…
This article uses a combination of three ideas from simulation to establish a nearly optimal polynomial upper bound for the joint density of the stable process and its associated supremum at a fixed time on the entire support of the joint…
We show that each set of $n\ge 2$ points in the plane in general position has a straight-line matching with at least $(5n+1)/27$ edges whose segments form a connected set, and such a matching can be computed in $O(n \log n)$ time. As an…
In a closed system, the total number of particles is fixed. We ask how much does this conservation law restrict the amount of entanglement that can be created. We derive a tight upper bound on the bipartite entanglement entropy in closed…
Recently, Gilmer proved the first constant lower bound for the union-closed sets conjecture via an information-theoretic argument. The heart of the argument is an entropic inequality involving the OR function of two i.i.d.\ binary vectors,…
Refining an existing counting argument, we provide an improved upper bound for the number of 1324-avoiding permutations of a given length.
This paper introduces a maximum likelihood estimator of the value of job amenities and labor productivity in a single matching market based on the observation of equilibrium matches and wages. The estimation procedure simultaneously fits…
We consider equilibrium one-on-one conversations between neighbors on a circular table, with the goal of assessing the likelihood of a (perhaps) familiar situation: sitting at a table where both of your neighbors are talking to someone…
In this paper we consider stable matchings subject to assignment constraints. These are matchings that require certain assigned pairs to be included, insist that some other assigned pairs are not, and, importantly, are stable. Our main…
We show that every cubic bridgeless graph with n vertices has at least 3n/4-10 perfect matchings. This is the first bound that differs by more than a constant from the maximal dimension of the perfect matching polytope.