English

Cycles in Austrian Solitaire

Combinatorics 2024-04-11 v4

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.

Cite

@article{arxiv.2304.10917,
  title  = {Cycles in Austrian Solitaire},
  author = {Philip Mummert},
  journal= {arXiv preprint arXiv:2304.10917},
  year   = {2024}
}

Comments

12 pages, 1 figure. Version update: adopted standard notation; clarified some details

R2 v1 2026-06-28T10:13:38.057Z