{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:30Z","timestamp":1753893810283,"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>We prove some new results about the combinatorial game \"Toads and Frogs\".  We give a finite number of recurrence relations for computing the values of all positions with exactly one $\\Box$.  We show that ${\\rm T}^{a}\\Box\\Box{\\rm F}^{a}$ is an infinitesimal for  $a\\geq 4$.  At the end, we make five new conjectures and describe possible future work.<\/jats:p>","DOI":"10.37236\/554","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T22:52:06Z","timestamp":1578696726000},"source":"Crossref","is-referenced-by-count":0,"title":["Further Hopping with Toads and Frogs"],"prefix":"10.37236","volume":"18","author":[{"given":"Thotsaporn \"Aek\"","family":"Thanatipanonda","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,3,24]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p67\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p67\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T18:15:00Z","timestamp":1579284900000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p67"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,3,24]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/554","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,3,24]]},"article-number":"P67"}}