{"title":"有$2^n-1$$芯片的二叉树上的标签芯片发射","authors":"Gregg Musiker, Son Nguyen","doi":"10.1007/s00026-023-00680-0","DOIUrl":null,"url":null,"abstract":"<p>We study labeled chip-firing on binary trees starting with <span>\\(2^n-1\\)</span> chips initially placed at the root. We prove a sorting property of terminal configurations of the process. We also analyze the end game moves poset and prove that this poset is a modular lattice.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Labeled Chip-Firing on Binary Trees with $$2^n-1$$ Chips\",\"authors\":\"Gregg Musiker, Son Nguyen\",\"doi\":\"10.1007/s00026-023-00680-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We study labeled chip-firing on binary trees starting with <span>\\\\(2^n-1\\\\)</span> chips initially placed at the root. We prove a sorting property of terminal configurations of the process. We also analyze the end game moves poset and prove that this poset is a modular lattice.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-12-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00026-023-00680-0\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00026-023-00680-0","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Labeled Chip-Firing on Binary Trees with $$2^n-1$$ Chips
We study labeled chip-firing on binary trees starting with \(2^n-1\) chips initially placed at the root. We prove a sorting property of terminal configurations of the process. We also analyze the end game moves poset and prove that this poset is a modular lattice.
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