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- W3103253701 abstract "We have known that most sequences in $mathcal{M}={1,2,dots, M}$ with length $n$ will miss $Me^{-lambda}$ of the total numbers of ${1,2,dots,M}$ as the ratio $n/M$ tends to $lambda$. Now we consider a more general case where the numbers in ${1,2,dots,M}$ are achieved exactly k times by a 'random' sequence $f(1), f(2),dots,f(n)$. We show that if $n/Mrightarrow lambda$, then the limit has a Poisson distribution, that is, the proportion of sequences for which some number in $mathcal{M}$ is achieved exactly $k$ times has the limit $frac{lambda^k}{k!}e^{-lambda}$. We conjecture that this is the behavior of the factorial mapping modulo a prime and present a few supporting arguments." @default.
- W3103253701 created "2020-11-23" @default.
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- W3103253701 date "2020-11-15" @default.
- W3103253701 modified "2023-09-27" @default.
- W3103253701 title "Factorials $pmod p$ and the average of modular mappings" @default.
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