Neighborliness Of The Symmetric Moment Curve
dc.contributor.author | Barvinok, Alexander | |
dc.contributor.author | Lee, Seung Jin | |
dc.contributor.author | Novik, Isabella | |
dc.date.accessioned | 2020-01-13T15:04:12Z | |
dc.date.available | 2020-01-13T15:04:12Z | |
dc.date.issued | 2013-01 | |
dc.identifier.citation | Barvinok, Alexander; Lee, Seung Jin; Novik, Isabella (2013). "Neighborliness Of The Symmetric Moment Curve." Mathematika 59(1): 223-249. | |
dc.identifier.issn | 0025-5793 | |
dc.identifier.issn | 2041-7942 | |
dc.identifier.uri | https://hdl.handle.net/2027.42/152540 | |
dc.description.abstract | We consider the convex hull ℬk of the symmetric moment curve Uk(t)=(cos t,sin t,cos 3t,sin 3t,…,cos (2k−1)t,sin (2k−1)t) in ℝ2k, where t ranges over the unit circle S=R/2πR. The curve Uk(t) is locally neighborly: as long as t1,…,tk lie in an open arc of S of a certain length ϕk>0, the convex hull of the points Uk (t1),…,Uk (tk) is a face of ℬk. We characterize the maximum possible length ϕk, proving, in particular, that ϕk >π/2 for all k and that the limit of ϕk is π/2 as k grows. This allows us to construct centrally symmetric polytopes with a record number of faces. | |
dc.publisher | London Mathematical Society | |
dc.publisher | Wiley Periodicals, Inc. | |
dc.subject.other | 26C10 (secondary) | |
dc.subject.other | 52B12 (primary) | |
dc.subject.other | 52A20 | |
dc.title | Neighborliness Of The Symmetric Moment Curve | |
dc.type | Article | |
dc.rights.robots | IndexNoFollow | |
dc.subject.hlbsecondlevel | Mathematics | |
dc.subject.hlbtoplevel | Science | |
dc.description.peerreviewed | Peer Reviewed | |
dc.description.bitstreamurl | https://deepblue.lib.umich.edu/bitstream/2027.42/152540/1/mtks0025579312000010.pdf | |
dc.identifier.doi | 10.1112/S0025579312000010 | |
dc.identifier.source | Mathematika | |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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