{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,30]],"date-time":"2026-01-30T23:30:11Z","timestamp":1769815811471,"version":"3.49.0"},"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>Given a space $\\Omega$ endowed with symmetry, we define $ms(\\Omega, r)$ to be the maximum of $m$ such that for any $r$-coloring of $\\Omega$ there exists a monochromatic symmetric set of size at least $m$. We consider a wide range of spaces $\\Omega$ including the discrete and continuous segments $\\{1, \\ldots, n\\}$ and $[0,1]$ with central symmetry, geometric figures with the usual symmetries of Euclidean space, and Abelian groups with a natural notion of central symmetry. We observe that $ms(\\{1, \\ldots, n\\}, r)$ and $ms([0,1], r)$ are closely related, prove lower and upper bounds for $ms([0,1], 2)$, and find asymptotics of $ms([0,1], r)$ for $r$ increasing. The exact value of $ms(\\Omega, r)$ is determined for figures of revolution, regular polygons, and multi-dimensional parallelopipeds. We also discuss problems of a slightly different flavor and, in particular, prove that the minimal $r$ such that there exists an $r$-coloring of the $k$-dimensional integer grid without infinite monochromatic symmetric subsets is $k+1$.<\/jats:p>","DOI":"10.37236\/1530","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:02:59Z","timestamp":1578708179000},"source":"Crossref","is-referenced-by-count":2,"title":["A Ramsey Treatment of Symmetry"],"prefix":"10.37236","volume":"7","author":[{"given":"T.","family":"Banakh","sequence":"first","affiliation":[]},{"given":"O.","family":"Verbitsky","sequence":"additional","affiliation":[]},{"given":"Ya.","family":"Vorobets","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2000,8,15]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v7i1r52\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v7i1r52\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:22:12Z","timestamp":1579324932000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v7i1r52"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,8,15]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2000,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1530","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,8,15]]},"article-number":"R52"}}