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- W2607887506 abstract "We introduce emph{$p_n$-random $q_n$-proportion Bulgarian solitaire} ($0<p_n,q_nle 1$), played on $n$ cards distributed in piles. In each pile, a number of cards equal to the proportion $q_n$ of the pile size rounded upward to the nearest integer are candidates to be picked. Each candidate card is picked with probability $p_n$, independently of other candidate cards. This generalizes Popov's random Bulgarian solitaire, in which there is a single candidate card in each pile. Popov showed that a triangular limit shape is obtained for a fixed $p$ as $n$ tends to infinity. Here we let both $p_n$ and $q_n$ vary with $n$. We show that under the conditions $q_n^2 p_n n/{log n}rightarrow infty$ and $p_n q_n rightarrow 0$ as $ntoinfty$, the $p_n$-random $q_n$-proportion Bulgarian solitaire has an exponential limit shape." @default.
- W2607887506 created "2017-05-05" @default.
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- W2607887506 date "2017-03-21" @default.
- W2607887506 modified "2023-09-27" @default.
- W2607887506 title "An exponential limit shape of random $q$-proportion Bulgarian solitaire" @default.
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