{"paper":{"title":"Limit shapes of stable configurations of a generalized Bulgarian solitaire","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jonas Sj\\\"ostrand, Kimmo Eriksson, Markus Jonsson","submitted_at":"2017-03-21T09:00:28Z","abstract_excerpt":"Bulgarian solitaire is played on $n$ cards divided into several piles; a move consists of picking one card from each pile to form a new pile. In a recent generalization, $\\sigma$-Bulgarian solitaire, the number of cards you pick from a pile is some function $\\sigma$ of the pile size, such that you pick $\\sigma(h)\\le h$ cards from a pile of size $h$. Here we consider a special class of such functions. Let us call $\\sigma$ well-behaved if $\\sigma(1)=1$ and if both $\\sigma(h)$ and $h-\\sigma(h)$ are non-decreasing functions of $h$. Well-behaved $\\sigma$-Bulgarian solitaire has a geometric interpre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07099","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}