{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:39:15Z","timestamp":1787323155050,"version":"build-2736575974"},"reference-count":28,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"DOI":"10.13039\/501100014398","name":"Mathematisches Forschungsinstitut Oberwolfach","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100014398","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100002261","name":"\u0420\u043e\u0441\u0441\u0438\u0439\u0441\u043a\u0438\u0439 \u0424\u043e\u043d\u0434 \u0424\u0443\u043d\u0434\u0430\u043c\u0435\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u0445 \u0418\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u043d\u0438\u0439","doi-asserted-by":"publisher","award":["20-01-00070"],"award-info":[{"award-number":["20-01-00070"]}],"id":[{"id":"10.13039\/501100002261","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004564","name":"Ministarstvo Prosvete, Nauke i Tehnolo\u0161kog Razvoja","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004564","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>We prove several versions of Alon's necklace-splitting theorem, subject to additional constraints, as illustrated by the following results. (1) The \u201calmost equicardinal necklace-splitting theorem\u201d claims that, without increasing the number of cuts, one guarantees the existence of a fair splitting such that each thief is allocated almost the same number of pieces of the necklace (including \u201cdegenerate pieces\u201d if they exist), provided the number of thieves $r=p^\\nu$ is a prime power. By \u201calmost the same\u201d we mean that for each pair of thieves one of them can be given at most one piece more (one piece less) than the other. (2) The \u201cbinary splitting theorem\u201d claims that if $r=2^d$ and the thieves are associated with the vertices of a $d$-cube, then, without increasing the number of cuts, one can guarantee the existence of a fair splitting such that adjacent pieces are allocated to thieves that share an edge of the cube. This result provides a positive answer to the \u201cbinary splitting necklace conjecture\u201d in the case $r=2^d$ from Conjecture 2.11 in [M. Asada et al., SIAM J. Discrete Math., 32 (2018), pp. 591--610]. (3) An interesting variation arises when the thieves have their own individual preferences. We prove several envy-free, fair necklace-splitting theorems of various level of generality, as illustrated by the envy-free versions of (a) Alon's original necklace-splitting theorem, (b) the almost equicardinal splitting theorem, and (c) the binary splitting theorem, etc.<\/jats:p>","DOI":"10.1137\/20m1331949","type":"journal-article","created":{"date-parts":[[2021,6,14]],"date-time":"2021-06-14T12:38:41Z","timestamp":1623674321000},"page":"1268-1286","source":"Crossref","is-referenced-by-count":5,"title":["Splitting Necklaces, with Constraints"],"prefix":"10.1137","volume":"35","author":[{"given":"Du\u0161ko","family":"Joji\u0107","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gaiane","family":"Panina","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rade","family":"\u017divaljevi\u0107","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,6,14]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/0001-8708(87)90055-7"},{"key":"atypb2","first-page":"1421","author":"Alon N.","year":"1990","journal-title":"Springer-Verlag"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1145\/1150334.1150336"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1137\/17M1116210"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1112\/mtk.12059"},{"key":"atypb6","first-page":"1819","author":"Bj\u00f6rner A.","year":"1995","journal-title":"Amsterdam"},{"key":"atypb7","doi-asserted-by":"crossref","first-page":"735","DOI":"10.4171\/dm\/544","volume":"21","author":"Blagojevi\u0107 P. V. M.","year":"2016","journal-title":"Doc. Math."},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1090\/tran\/7528"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1112\/blms\/bdu049"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1007\/BF01769865"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2005.06.005"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2019.103004"},{"key":"atypb13","first-page":"1","volume":"104","author":"Joji\u0107 D.","year":"2018","journal-title":"S.)"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-021-2087-3"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1007\/s10801-017-0743-9"},{"key":"atypb16","doi-asserted-by":"crossref","unstructured":"J. Matou\u0161ek,\n                      Using the Borsuk-Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry\n                      , Springer-Verlag, Berlin, Heidelberg, 2008.","DOI":"10.1007\/978-3-540-76649-0"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-019-1939-6"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1016\/0001-8708(78)90058-0"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1007\/BF02717729"},{"key":"atypb20","doi-asserted-by":"crossref","unstructured":"E. Segal-Halevi,\n                      Fairly dividing a cake after some parts were burnt in the oven\n                      , in Proceedings of the 17th International Conference on Autonomous Agents and MultiAgent Systems, AAMAS '18, Richland, SC, 2018, International Foundation for Autonomous Agents and Multiagent Systems, pp. 1276-1284.","DOI":"10.65109\/MMMC8499"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.1980.11995109"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1007\/BF02308547"},{"key":"atypb23","unstructured":"S. T. Vre\u0107ica and R. T. \u017divaljevi\u0107,\n                      Hyperplane Mass Equipartition Problem and the Shielding Functions of Ramos\n                      , preprint,https:\/\/arxiv.org\/abs\/1508.01552, 2016."},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1007\/BF02189327"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(80)90225-5"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.12775\/TMNA.2015.004"},{"key":"atypb27","first-page":"551","author":"\u017divaljevi\u0107 R.","year":"2017","journal-title":"Boca Raton, FL"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2004.12.002"}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/20M1331949","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:44:47Z","timestamp":1787319887000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/20M1331949"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":28,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1137\/20M1331949"],"URL":"https:\/\/doi.org\/10.1137\/20m1331949","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1]]}}}