{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:32:40Z","timestamp":1787322760939,"version":"build-2736575974"},"reference-count":8,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS1661063"],"award-info":[{"award-number":["DMS1661063"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"publisher","award":["522400"],"award-info":[{"award-number":["522400"]}],"id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"publisher","award":["AD"],"award-info":[{"award-number":["AD"]}],"id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:p>The game of plates and olives was originally formulated by Nicolaescu and encodes the evolution of the topology of the sublevel sets of Morse functions. We consider a random variant of this game. The process starts with an empty table. There are four different types of moves: (1) add a new plate to the table, (2) combine two plates and their olives onto one plate, removing the second plate from the table, (3) add an olive to a plate, and (4) remove an olive from a plate. We show that with high probability the number of olives is linear as the total number of moves goes to infinity. Furthermore, we prove that the number of olives is concentrated around its expectation.<\/jats:p>","DOI":"10.1137\/18m1177780","type":"journal-article","created":{"date-parts":[[2019,7,2]],"date-time":"2019-07-02T14:51:01Z","timestamp":1562079061000},"page":"1216-1227","source":"Crossref","is-referenced-by-count":0,"title":["A Random Variant of the Game of Plates and Olives"],"prefix":"10.1137","volume":"33","author":[{"given":"Andrzej","family":"Dudek","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sean","family":"English","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alan M.","family":"Frieze","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2019,7,2]]},"reference":[{"key":"atypb1","first-page":"26","author":"Carroll T.","year":"2019","journal-title":"Electron. J. Combin."},{"key":"atypb2","doi-asserted-by":"crossref","unstructured":"A. Frieze and M. Karo\u0144ski,\n                      Introduction to Random Graphs\n                      , Cambridge University Press, Cambridge, 2015.","DOI":"10.1017\/CBO9781316339831"},{"key":"atypb3","doi-asserted-by":"crossref","unstructured":"A. Frieze and W. Pegden,\n                      Travelling in randomly embedded random graphs\n                      , Proceedings of RANDOM 2017, to appear.","DOI":"10.1002\/rsa.20832"},{"key":"atypb4","doi-asserted-by":"crossref","unstructured":"R. Gallager,\n                      Stochastic Processes. Theory for Applications\n                      , Cambridge University Press, Cambridge, 2013; also available online fromhttp:\/\/www.rle.mit.edu\/rgallager\/documents\/CountMarkov.pdf.","DOI":"10.1017\/CBO9781139626514"},{"key":"atypb6","volume":"3","author":"Gould H. W.","journal-title":"Table III: Basic Algebraic Techniques, J. Quaintance, ed., http:\/\/www.math.wvu.edu\/ gould\/"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1112\/S0010437X08003680"},{"key":"atypb8","first-page":"263966","author":"Nicolaescu L. I.","year":"2017","journal-title":"MathOverflow Question"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1515\/integers-2012-0014"}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/18M1177780","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:25:20Z","timestamp":1787318720000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/18M1177780"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1]]},"references-count":8,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2019,1]]}},"alternative-id":["10.1137\/18M1177780"],"URL":"https:\/\/doi.org\/10.1137\/18m1177780","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1]]}}}