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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.03921 |
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| _version_ | 1866916384584237056 |
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| author | Enciso-Alva Cesar, Julio |
| author_facet | Enciso-Alva Cesar, Julio |
| contents | Consider a fair lottery over the natural numbers in which the selected number is removed. This lottery is iterated countably infinite times, with a known ratio of iterations to natural numbers. Removed numbers are not replaced. The natural numbers are partitioned into two sets with a given ratio of elements, which is tracked along each iteration of the lottery.
Hess and Polisetty considered and investigated such a process and reported the expected values of the densities for some particular cases.
In this work, we provide a novel framework for computing these expected densities using infinite matrices. The results presented in this work generalize previous results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_03921 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Expected Natural Density of Countable Sets after Infinitely Iterated de Finetti Lotteries, Computed via Matrix Decomposition Enciso-Alva Cesar, Julio Combinatorics Consider a fair lottery over the natural numbers in which the selected number is removed. This lottery is iterated countably infinite times, with a known ratio of iterations to natural numbers. Removed numbers are not replaced. The natural numbers are partitioned into two sets with a given ratio of elements, which is tracked along each iteration of the lottery. Hess and Polisetty considered and investigated such a process and reported the expected values of the densities for some particular cases. In this work, we provide a novel framework for computing these expected densities using infinite matrices. The results presented in this work generalize previous results. |
| title | Expected Natural Density of Countable Sets after Infinitely Iterated de Finetti Lotteries, Computed via Matrix Decomposition |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2409.03921 |