{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:48Z","timestamp":1753893828275,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Positional games are a well-studied class of combinatorial games. In\u00a0their usual form, two players take turns to play moves in a set\u00a0('the board'), and certain subsets are designated as 'winning': the\u00a0first person to occupy such a set wins the game. For these games, it\u00a0is well known that (with correct play) the game cannot be a\u00a0second-player win.In the avoidance (or mis\u00e8re) form, the first person to occupy\u00a0such a set loses the game. Here it would be natural to expect that\u00a0the game cannot be a first-player win, at least if the game is\u00a0transitive, meaning that all points of the board look the same. Our\u00a0main result is that, contrary to this expectation, there are\u00a0transitive games that are first-player wins, for all board sizes\u00a0which are not prime or a power of 2.Further, we show that such games can have additional properties such\u00a0as stronger transitivity conditions, fast winning times, and 'small'\u00a0winning sets.\u00a0\u00a0\u00a0<\/jats:p>","DOI":"10.37236\/6299","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:59:03Z","timestamp":1578671943000},"source":"Crossref","is-referenced-by-count":0,"title":["Transitive Avoidance Games"],"prefix":"10.37236","volume":"24","author":[{"given":"J. Robert","family":"Johnson","sequence":"first","affiliation":[]},{"given":"Imre","family":"Leader","sequence":"additional","affiliation":[]},{"given":"Mark","family":"Walters","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2017,3,31]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i1p61\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i1p61\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:03:10Z","timestamp":1579237390000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v24i1p61"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,3,31]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2017,1,20]]}},"URL":"https:\/\/doi.org\/10.37236\/6299","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2017,3,31]]},"article-number":"P1.61"}}