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dc.contributor.authorŽivaljević, Radeen
dc.date.accessioned2020-04-12T18:03:58Z-
dc.date.available2020-04-12T18:03:58Z-
dc.date.issued2008-01-01en
dc.identifier.issn0002-9947en
dc.identifier.urihttp://researchrepository.mi.sanu.ac.rs/handle/123456789/299-
dc.description.abstractA well-known problem of B. Grünbaum (1960) asks whether for every continuous mass distribution (measure) dμ = f dm on ℝn there exist n hyperplanes dividing ℝn into 2n parts of equal measure. It is known that the answer is positive in dimension n ≥ 3 (see H. Hadwiger (1966)) and negative for n = 5 (see D. Avis (1984) and E. Ramos (1996)). We give a partial solution to Grünbaum's problem in the critical dimension n = 4 by proving that each measure μin ℝ4 admits an equipartition by 4 hyperplanes, provided that it is symmetric with respect to a 2-dimensional affine subspace L of ℝ4. Moreover we show, by computing the complete obstruction in the relevant group of normal bordisms, that without the symmetry condition, a naturally associated topological problem has a negative solution. The computation is based on Koschorke's exact singularity sequence (1981) and the remarkable properties of the essentially unique, balanced binary Gray code in dimension 4; see G. C. Tootill (1956) and D. E. Knuth (2001). © 2007 American Mathematical Society.en
dc.publisherAmerican Mathematical Society-
dc.relationSerbian Ministry of Science and Technology, Grant no. 1643-
dc.relation.ispartofTransactions of the American Mathematical Societyen
dc.subjectGeometric combinatorics | Gray codes | Partitions of massesen
dc.titleEquipartitions of measures in ℝ4en
dc.typeArticleen
dc.identifier.doi10.1090/S0002-9947-07-04294-8en
dc.identifier.scopus2-s2.0-77950952045en
dc.contributor.affiliationMathematical Institute of the Serbian Academy of Sciences and Arts-
dc.relation.firstpage153en
dc.relation.lastpage169en
dc.relation.issue1en
dc.relation.volume360en
dc.description.rankM21-
item.openairetypeArticle-
item.cerifentitytypePublications-
item.fulltextNo Fulltext-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.grantfulltextnone-
crisitem.author.orcid0000-0001-9801-8839-
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