{"title":"Acute Tours in the Plane","authors":"Ahmad Biniaz","doi":"10.1007/s00454-023-00486-0","DOIUrl":"https://doi.org/10.1007/s00454-023-00486-0","url":null,"abstract":"","PeriodicalId":356162,"journal":{"name":"Discrete and Computational Geometry","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135290456","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"An Application of Shadow Systems to Mahler’s Conjecture","authors":"FradeliziMatthieu, MeyerMathieu, ZvavitchArtem","doi":"10.5555/2349130.2349140","DOIUrl":"https://doi.org/10.5555/2349130.2349140","url":null,"abstract":"We elaborate on the use of shadow systems to prove a particular case of the conjectured lower bound of the volume product $mathcal{P}(K)=min_{zinoperatorname{int}(K)}|K||K^{z}|$, where K⊂ℝ n is...","PeriodicalId":356162,"journal":{"name":"Discrete and Computational Geometry","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117295526","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Carathéodory-type Theorems à la Bárány","authors":"BokowskiJürgen, BrachoJavier, StrauszRicardo","doi":"10.5555/1937149.1937153","DOIUrl":"https://doi.org/10.5555/1937149.1937153","url":null,"abstract":"We generalise the famous Helly–Lovasz theorem leading to a generalisation of the Barany–Caratheodory theorem for oriented matroids in dimension ≤3. We also provide a non-metric proof of the latter ...","PeriodicalId":356162,"journal":{"name":"Discrete and Computational Geometry","volume":"91 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124654070","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Constrained Minkowski Sums","authors":"BernholtThorsten, EisenbrandFriedrich, HofmeisterThomas","doi":"10.5555/3116258.3116372","DOIUrl":"https://doi.org/10.5555/3116258.3116372","url":null,"abstract":"In this paper, we introduce the notion of a constrained Minkowski sum: for two (finite) point-sets P,Q⊆ź2 and a set of k inequalities Axźb, it is defined as the point-set (PźQ)Axźb={x=p+qźpźP,qźQ,A...","PeriodicalId":356162,"journal":{"name":"Discrete and Computational Geometry","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122565590","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Large Cells in Poisson–Delaunay Tessellations","authors":"HugDaniel, SchneiderRolf","doi":"10.5555/1006012.1006014","DOIUrl":"https://doi.org/10.5555/1006012.1006014","url":null,"abstract":"It is proved that the shape of the typical cell of a Delaunay tessellation, derived from a stationary Poisson point process in d-dimensional Euclidean space, tends to the shape of a regular simplex...","PeriodicalId":356162,"journal":{"name":"Discrete and Computational Geometry","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115540054","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Quantizing Using Lattice Intersections","authors":"N. Sloane, B. Beferull-Lozano","doi":"10.1007/978-3-642-55566-4_38","DOIUrl":"https://doi.org/10.1007/978-3-642-55566-4_38","url":null,"abstract":"","PeriodicalId":356162,"journal":{"name":"Discrete and Computational Geometry","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125418596","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Recent progress on polytopes","authors":"G. Ziegler","doi":"10.1090/conm/223/03151","DOIUrl":"https://doi.org/10.1090/conm/223/03151","url":null,"abstract":"Novel phthalimides substituted by alkenylamino groups, processes for their preparation and hot-curable mixtures which are stable on storage and contain at least one phthalimide according to the invention and a polyimide which has at least two groupings containing a C=C double bond are described. These hot-curable mixtures which are stable on storage are distinguished by improved processing characteristics, in particular a prolonged pot life, and are suitable for the production of various mouldings and especially also for the production of complicated castings.","PeriodicalId":356162,"journal":{"name":"Discrete and Computational Geometry","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131140986","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Open Problems in the Combinatorics of Visibility and Illumination","authors":"J. O'Rourke","doi":"10.1090/conm/223/03140","DOIUrl":"https://doi.org/10.1090/conm/223/03140","url":null,"abstract":"1991 Primary 52C99. Visibility, illumination, visibility graphs, computational geometry. Supported by NSF grant CCR-9421670. URL: . The art gallery theorem,\" that 3 guards su ce and are sometimes necessary to visually cover a polygon of vertices [ ] [ ], typi es the interplay between geometry and combinatorics in a wide variety of subsequent results. The open problems in this collection are intellectual kins to these art gallery-like results. The problems represent a personal selection from the frontier of research on the combinatorics of visibility; no attempt is made to be comprehensive. Updates will be maintained on the Web. In general, a point can , is to, or a point if the line segment is not obstructed. (The metaphors of visibility\" and illumination\" are used interchangeably.) Often this means that cannot contain any point of a set of obstacles, but sometimes is permitted to contain boundary points of the obstacles (line-of-sight grazing contact). Other nuances to the de nition of visibility are appropriate for certain problems, and will be detailed below. Throughout will be used to denote the constant of proportionality for quantities of the form + for some constant , where is the primary input variable (e.g., the number of vertices). Precise fractional bounds will be supplemented by their approximate decimal equivalents.","PeriodicalId":356162,"journal":{"name":"Discrete and Computational Geometry","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115785408","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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