A note on random Bulgarian solitaire
نویسنده
چکیده
We consider a stochastic variant of the game of Bulgarian solitaire [9]. For the stationary measure of the random Bulgarian solitaire, we prove that most of its mass is concentrated on (roughly) triangular configurations of certain type.
منابع مشابه
Random Bulgarian solitaire
We consider a stochastic variant of the game of Bulgarian solitaire [9]. For the stationary measure of the random Bulgarian solitaire, we prove that most of its mass is concentrated on (roughly) triangular configurations of certain type.
متن کاملThe Bulgarian Solitaire and the Mathematics around It
The Bulgarian solitaire is a mathematical card game played by one person. A pack of n cards is divided into several decks (or “piles”). Each move consists of the removing of one card from each deck and collecting the removed cards to form a new deck. The game ends when the same position occurs twice. It has turned out that when n = k(k + 1)/2 is a triangular number, the game reaches the same st...
متن کاملShift-Induced Dynamical Systems on Partitions and Compositions
The rules of “Bulgarian solitaire” are considered as an operation on the set of partitions to induce a finite dynamical system. We focus on partitions with no preimage under this operation, known as Garden of Eden points, and their relation to the partitions that are in cycles. These are the partitions of interest, as we show that starting from the Garden of Eden points leads through the entire...
متن کاملExact Enumeration of Garden of Eden Partitions
We give two proofs for a formula that counts the number of partitions of n that have rank −2 or less (which we call Garden of Eden partitions). These partitions arise naturally in analyzing the game Bulgarian solitaire, summarized in Section 1. Section 2 presents a generating function argument for the formula based on Dyson’s original paper where the rank of a partition is defined. Section 3 gi...
متن کاملColumn-to-row Operations on Partitions: the Envelopes
Conjugation and the Bulgarian solitaire move are considered as extreme cases of several column-to-row operations on integer partitions. Each operation generates a state diagram on the partitions of n, which leads to the questions: How many Garden of Eden states are there? How many cycle states? How many connected components? All of these questions are answered for partitions of n when at least ...
متن کامل