6 papers
Why Distance Two Is Exceptional for Poisson-Binomial Point Probabilities
Igor Kleiner
Let be a finite sum of independent Bernoulli random variables. We ask how large the mean must be before the atom at can strictly exceed the atom at . For the threshold…
The Last Isolated Vertex in Random-Order Uncovering of Cycles and Their Powers: Exact Enumeration and Weibull Limits
Igor Kleiner
Let the vertices of a graph be revealed one at a time in a uniformly random order, and let the last-isolation time be the last time at which the induced graph on the revealed verti…
Initial Runs in Integer Compositions: Lambert Series and Generalized Divisor Sums
Igor Kleiner
We study the initial run of equal adjacent parts in an integer composition. For a composition alpha, let P(alpha) be the common value of the parts in the initial run, let K(alpha)…
One Empty Locker and Two Inspections: An Exact Optimal Team Strategy
Igor Kleiner, David Perry
We study a cooperative search game with lockers, labelled objects, one empty locker, and players. Player seeks object and may inspect at most two lockers; t…
An Exact Solution of the Two-Ball Multi-Look Search Game with Three Boxes and Heterogeneous Costs
Igor Kleiner
A Hider distributes two identical balls among three boxes whose search costs satisfy . A Searcher opens boxes adaptively until both balls are found; every opening in…
A Decomposition Property for an Queue with Vacations
Igor Kleiner, Esther Frostig, David Perry
We introduce a queueing system that alternates between two modes, so-called {\it working mode} and {\it vacation mode}. During the working mode the system runs as an qu…