{"id":"https://openalex.org/W2143945112","doi":"https://doi.org/10.1137/080741926","title":"On Ruckle's Conjecture on Accumulation Games","display_name":"On Ruckle's Conjecture on Accumulation Games","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2143945112","doi":"https://doi.org/10.1137/080741926","mag":"2143945112"},"language":"en","primary_location":{"id":"doi:10.1137/080741926","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080741926","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023618082","display_name":"Steve Alpern","orcid":"https://orcid.org/0000-0002-0095-4299"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Steve Alpern","raw_affiliation_strings":["[email\u00a0protected]#TAB#"],"affiliations":[{"raw_affiliation_string":"[email\u00a0protected]#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091477617","display_name":"Robbert Fokkink","orcid":"https://orcid.org/0000-0001-8347-4110"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Robbert Fokkink","raw_affiliation_strings":["[email\u00a0protected]#TAB#"],"affiliations":[{"raw_affiliation_string":"[email\u00a0protected]#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008290083","display_name":"Ken Kikuta","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ken Kikuta","raw_affiliation_strings":["[email\u00a0protected]#TAB#"],"affiliations":[{"raw_affiliation_string":"[email\u00a0protected]#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5023618082"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.3762,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.87676056,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"48","issue":"8","first_page":"5073","last_page":"5083"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9916999936103821,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9904999732971191,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.8674572706222534},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8413347005844116},{"id":"https://openalex.org/keywords/bounding-overwatch","display_name":"Bounding overwatch","score":0.7616853713989258},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6826253533363342},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.6384098529815674},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40652623772621155},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09552311897277832},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07650479674339294},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.04438483715057373}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.8674572706222534},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8413347005844116},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.7616853713989258},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6826253533363342},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.6384098529815674},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40652623772621155},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09552311897277832},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07650479674339294},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.04438483715057373}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/080741926","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080741926","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.218.6093","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.218.6093","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cdam.lse.ac.uk/Reports/Files/cdam-2008-20.pdf","raw_type":"text"},{"id":"pmh:oai:eprints.lse.ac.uk:33599","is_oa":false,"landing_page_url":"http://eprints.lse.ac.uk/33599/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401593","display_name":"London School of Economics and Political Science Research Online (London School of Economics and Political Science)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I909854389","host_organization_name":"London School of Economics and Political Science","host_organization_lineage":["https://openalex.org/I909854389"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:tudelft.nl:uuid:677c2fee-1802-4ca2-9bf1-0cb678351cc5","is_oa":false,"landing_page_url":"http://resolver.tudelft.nl/uuid:677c2fee-1802-4ca2-9bf1-0cb678351cc5","pdf_url":null,"source":{"id":"https://openalex.org/S4306400906","display_name":"Research Repository (Delft University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I98358874","host_organization_name":"Delft University of Technology","host_organization_lineage":["https://openalex.org/I98358874"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"journal article"},{"id":"pmh:oai:wrap.warwick.ac.uk:77280","is_oa":false,"landing_page_url":"http://wrap.warwick.ac.uk/77280/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400665","display_name":"Warwick Research Archive Portal (University of Warwick)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39555362","host_organization_name":"University of Warwick","host_organization_lineage":["https://openalex.org/I39555362"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Decent work and economic growth","id":"https://metadata.un.org/sdg/8","score":0.44999998807907104}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W87981002","https://openalex.org/W143270080","https://openalex.org/W657644399","https://openalex.org/W1538925978","https://openalex.org/W1911815410","https://openalex.org/W1970075652","https://openalex.org/W1990747572","https://openalex.org/W2019935404","https://openalex.org/W2023135717","https://openalex.org/W2037884978","https://openalex.org/W2040812865","https://openalex.org/W2045485109","https://openalex.org/W2053777683","https://openalex.org/W2066502241","https://openalex.org/W2067335999","https://openalex.org/W2072156568","https://openalex.org/W2146359763","https://openalex.org/W4238472918","https://openalex.org/W4240383795","https://openalex.org/W4243611788"],"related_works":["https://openalex.org/W587735977","https://openalex.org/W1978142926","https://openalex.org/W3157395178","https://openalex.org/W3166204570","https://openalex.org/W3121246613","https://openalex.org/W3194471551","https://openalex.org/W184455116","https://openalex.org/W2132137594","https://openalex.org/W4375956809","https://openalex.org/W1581373162"],"abstract_inverted_index":{"In":[0],"an":[1,52,59],"accumulation":[2],"game,":[3],"the":[4,17,24,36,45,73,81,99,110],"Hider":[5,29,54],"secretly":[6],"distributes":[7],"his":[8],"given":[9],"total":[10],"wealth":[11],"h":[12],"among":[13],"n":[14],"locations,":[15],"while":[16],"Searcher":[18,46],"picks":[19],"r":[20],"locations":[21,39,67],"and":[22,77,93,109],"confiscates":[23],"material":[25],"placed":[26],"there.":[27],"The":[28,95],"wins":[30],"if":[31],"what":[32],"is":[33,40,56],"left":[34],"at":[35,41,63],"remaining":[37],"$n-r$":[38],"least":[42],"1;":[43],"otherwise":[44],"wins.":[47],"Ruckle's":[48,107],"conjecture":[49,82,108],"says":[50],"that":[51],"optimal":[53],"strategy":[55],"to":[57],"put":[58],"equal":[60],"amount":[61],"$h/k$":[62],"k":[64],"randomly":[65],"chosen":[66],"for":[68,83],"some":[69],"k.":[70],"We":[71,102],"extend":[72],"work":[74],"of":[75,113,117,119],"Kikuta":[76],"Ruckle":[78],"by":[79],"proving":[80],"several":[84],"cases,":[85],"e.g.,":[86],"$r=2$":[87],"or":[88],"$n-2$;":[89],"$n\\leq7$;":[90],"$n=2r-1$;":[91],"$h\\leq2+1/\\,(n-r)$":[92],"$n\\leq2r$.":[94],"last":[96],"result":[97],"uses":[98],"Erd\u0151s\u2013Ko\u2013Rado":[100],"theorem.":[101],"establish":[103],"a":[104],"connection":[105],"between":[106],"Hoeffding":[111],"problem":[112],"bounding":[114],"tail":[115],"probabilities":[116],"sums":[118],"random":[120],"variables.":[121]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}