{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T18:29:57Z","timestamp":1649096997066},"reference-count":6,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2017,5]]},"abstract":"<jats:p> The Tarski number of a nonamenable group is the smallest number of pieces needed for a paradoxical decomposition of the group. Nonamenable groups of piecewise projective homeomorphisms were introduced in [N. Monod, Groups of piecewise projective homeomorphisms, Proc. Natl. Acad. Sci. 110(12) (2013) 4524\u20134527], and nonamenable finitely presented groups of piecewise projective homeomorphisms were introduced in [Y. Lodha and J. T. Moore, A finitely presented non amenable group of piecewise projective homeomorphisms, Groups, Geom. Dyn. 10(1) (2016) 177\u2013200]. These groups do not contain non-abelian free subgroups. In this paper, we prove that the Tarski number of all groups in both families is at most 25. In particular, we demonstrate the existence of a paradoxical decomposition with 25 pieces. <\/jats:p><jats:p> Our argument also applies to any group of piecewise projective homeomorphisms that contains as a subgroup the group of piecewise [Formula: see text] homeomorphisms of [Formula: see text] with rational breakpoints and an affine map that is a not an integer translation. <\/jats:p>","DOI":"10.1142\/s0218196717500151","type":"journal-article","created":{"date-parts":[[2017,4,11]],"date-time":"2017-04-11T07:50:35Z","timestamp":1491897035000},"page":"315-321","source":"Crossref","is-referenced-by-count":2,"title":["An upper bound for the Tarski numbers of nonamenable groups of piecewise projective homeomorphisms"],"prefix":"10.1142","volume":"27","author":[{"given":"Yash","family":"Lodha","sequence":"first","affiliation":[{"name":"EPFL SB MATH EGG, MA C3 584, (B\u00e2timent MA), Station 8, CH-1015 Lausanne, Switzerland"}]}],"member":"219","published-online":{"date-parts":[[2017,4,11]]},"reference":[{"issue":"19","key":"S0218196717500151BIB001","first-page":"677","volume":"300","author":"Carri\u00e8re Y.","year":"1985","journal-title":"C. R. Acad. Sci. Paris S\u00e9r. I Math."},{"issue":"1","key":"S0218196717500151BIB002","first-page":"57","volume":"224","author":"Ceccherini-Silberstein T.","year":"1999","journal-title":"Proc. Steklov Inst. Math."},{"key":"S0218196717500151BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2015.07.010"},{"key":"S0218196717500151BIB004","doi-asserted-by":"publisher","DOI":"10.4171\/GGD\/347"},{"key":"S0218196717500151BIB005","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1218426110"},{"issue":"4","key":"S0218196717500151BIB006","first-page":"199","volume":"35","author":"Ol\u2019shanskii A. Y.","year":"1980","journal-title":"Uspekhi Mat. Nauk"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196717500151","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T21:31:00Z","timestamp":1565127060000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196717500151"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,4,11]]},"references-count":6,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2017,3,20]]},"published-print":{"date-parts":[[2017,5]]}},"alternative-id":["10.1142\/S0218196717500151"],"URL":"https:\/\/doi.org\/10.1142\/s0218196717500151","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,4,11]]}}}