Igor Kleiner

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math.CO2026

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…

math.CO2026

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)…

math.CO2026

One Empty Locker and Two Inspections: An Exact Optimal Team Strategy

Igor Kleiner, David Perry

We study a cooperative search game with $N$ lockers, $N - 1$ labelled objects, one empty locker, and $N - 1$ players. Player $i$ seeks object $i$ and may inspect at most two lockers; t…