{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:25Z","timestamp":1753893865155,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We study a variation of Nim-type subtraction games, called Cumulative Subtraction (CS). Two players alternate in removing\u00a0pebbles out of a joint pile, and their actions add or remove points to a common score. We prove that the zero-sum outcome in optimal play of a CS with a finite number of possible actions is eventually periodic, with period $2s$, where $s$ is the size of the largest available action. This settles a conjecture by Stewart in his Ph.D. thesis (2011). Specifically, we find a quadratic bound, in the size of $s$, on when the outcome function must have become periodic. In case of exactly two possible actions, we give an explicit description of optimal play.<\/jats:p>","DOI":"10.37236\/7904","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T05:59:28Z","timestamp":1578635968000},"source":"Crossref","is-referenced-by-count":0,"title":["Cumulative Subtraction Games"],"prefix":"10.37236","volume":"26","author":[{"given":"Gal","family":"Cohensius","sequence":"first","affiliation":[]},{"given":"Urban","family":"Larsson","sequence":"additional","affiliation":[]},{"given":"Reshef","family":"Meir","sequence":"additional","affiliation":[]},{"given":"David","family":"Wahlstedt","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2019,12,20]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i4p52\/7983","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i4p52\/7983","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:00:12Z","timestamp":1579233612000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v26i4p52"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12,20]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2019,10,11]]}},"URL":"https:\/\/doi.org\/10.37236\/7904","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2019,12,20]]},"article-number":"P4.52"}}