Igor Kleiner

The Fragile Coupon Collector: Random Deadlines, Critical Fragility, and Optimal Sampling

We study coupon collection when each type is at risk of disappearing until its first observation, after which it becomes permanently safe. Sampling follows a fixed independent and identically distributed law. For uniform sampling and common fragility, the success probability is t...

Return-Growth Sequences: Euler Enumeration and Pattern Avoidance

A return-growth sequence is a restricted-growth word whose admissible range expands only when the word returns to a previously used value after leaving it; an adjacent repetition does not enlarge the range. Compressing maximal constant runs separates a word into a run skeleton ca...