Random sets and intersections
| Autor: | Handelman, David |
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| Rok vydání: | 2016 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | The following class of problems arose out of vain attempts to show that the Pascal's triangle adic transformation has trivial spectrum. Partition a set of size $N$ into sets of size $S \equiv S(N)$ (ignoring leftovers). What is the likelihood that a set of size $K \equiv K(N)$ will intersect each set in the partition in at least $R \equiv R(N)$ members (as $N$ increases)? Via elementary techniques and under reasonable hypotheses, we obtain an easy-to-use formula. Although different from the corresponding minimum problem for balls and bins (with $m = K$ balls and $n = N/S$ bins), under modest constraints, the asymptotic probabilities are the same. Comment: Comments solicited |
| Databáze: | arXiv |
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