Discrete Mathematics<\/em>, Volume 344, Issue 3, March 2021, 112256 https:\/\/doi.org\/10.1016\/j.disc.2020.112256<\/a>\u00a0arXiv<\/a><\/p>\n

I’ve previously written about the Namer-Claimer game<\/a>.\u00a0 I can now prove that the length of the game is with optimal play from each side, matching the greedy lower bound.\u00a0 The upper bound makes use of randomness, but in a very controlled way.\u00a0 Analysing a truly random strategy still seems like it will be very difficult.<\/p>\n

The proof brings up a surprising connection to the Ramsey theory of Hilbert cubes.<\/p>\n","protected":false},"excerpt":{"rendered":"

Discrete Mathematics, Volume 344, Issue 3, March 2021, 112256 https:\/\/doi.org\/10.1016\/j.disc.2020.112256\u00a0arXiv I’ve previously written about the Namer-Claimer game.\u00a0 I can now prove that the length of the game is with optimal play from each side, matching the greedy lower bound.\u00a0 The upper bound makes use of randomness, but in a very controlled way.\u00a0 Analysing a truly … <\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[3],"tags":[13,27,30],"_links":{"self":[{"href":"https:\/\/babarber.uk\/wp-json\/wp\/v2\/posts\/457"}],"collection":[{"href":"https:\/\/babarber.uk\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/babarber.uk\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/babarber.uk\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/babarber.uk\/wp-json\/wp\/v2\/comments?post=457"}],"version-history":[{"count":0,"href":"https:\/\/babarber.uk\/wp-json\/wp\/v2\/posts\/457\/revisions"}],"wp:attachment":[{"href":"https:\/\/babarber.uk\/wp-json\/wp\/v2\/media?parent=457"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/babarber.uk\/wp-json\/wp\/v2\/categories?post=457"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/babarber.uk\/wp-json\/wp\/v2\/tags?post=457"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}