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Yates-Grundy draw-by-draw sampling inclusion probabilities

Is there an efficient algorithm to calculate the inclusion probabilities (the probability that an item will be included in a sample) in the Yates-Grundy draw-by-draw sampling? … Sampling description: We have $n$ items each with probabilities $p_1, \dots, p_n$ of being selected in the first draw. …
Josef Ondrej's user avatar