Cycles in Austrian Solitaire

IF 1 3区数学 Q1 MATHEMATICS

European Journal of Combinatorics Pub Date : 2024-05-04 DOI:10.1016/j.ejc.2024.103978

Philip P. Mummert

引用次数: 0

Abstract

Austrian Solitaire is a variation of Bulgarian Solitaire. It may be described as a card game, a method of asset inventory management, or a discrete dynamical system on integer partitions. We prove that the limit cycles in Austrian Solitaire do not depend on the initial configuration; in other words, each state space is connected. We show that a full Farey sequence completely characterizes these unique (and balanced) cycles.

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奥地利接龙中的循环

奥地利接龙是保加利亚接龙的一种变体。它可以被描述为一种纸牌游戏、一种资产库存管理方法或一种整数分区上的离散动力系统。我们证明了奥地利接龙的极限循环不依赖于初始配置；换句话说，每个状态空间都是相连的。我们证明，一个完整的法雷序列完全表征了这些独特（且平衡）的循环。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

European Journal of Combinatorics 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

124

审稿时长

4-8 weeks

期刊介绍： The European Journal of Combinatorics is a high standard, international, bimonthly journal of pure mathematics, specializing in theories arising from combinatorial problems. The journal is primarily open to papers dealing with mathematical structures within combinatorics and/or establishing direct links between combinatorics and other branches of mathematics and the theories of computing. The journal includes full-length research papers on important topics.