Discrete & Computational Geometry最新文献

{"title":"Smooth Column Convex Polyominoes","authors":"T. Mansour, A. S. Shabani","doi":"10.1007/s00454-022-00405-9","DOIUrl":"https://doi.org/10.1007/s00454-022-00405-9","url":null,"abstract":"","PeriodicalId":50574,"journal":{"name":"Discrete & Computational Geometry","volume":"68 1","pages":"525 - 539"},"PeriodicalIF":0.8,"publicationDate":"2022-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45015275","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Efficient Quantisation and Weak Covering of High Dimensional Cubes","authors":"J. Noonan, A. Zhigljavsky","doi":"10.1007/s00454-022-00396-7","DOIUrl":"https://doi.org/10.1007/s00454-022-00396-7","url":null,"abstract":"","PeriodicalId":50574,"journal":{"name":"Discrete & Computational Geometry","volume":"68 1","pages":"540 - 565"},"PeriodicalIF":0.8,"publicationDate":"2022-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45518219","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Irrational Toric Varieties and Secondary Polytopes","authors":"A. Pi̇r, F. Sottile","doi":"10.1007/s00454-021-00334-z","DOIUrl":"https://doi.org/10.1007/s00454-021-00334-z","url":null,"abstract":"","PeriodicalId":50574,"journal":{"name":"Discrete & Computational Geometry","volume":"67 1","pages":"1053 - 1079"},"PeriodicalIF":0.8,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41652715","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Dirac–Goodman–Pollack Conjecture","authors":"A. Dumitrescu","doi":"10.1007/s00454-023-00487-z","DOIUrl":"https://doi.org/10.1007/s00454-023-00487-z","url":null,"abstract":"","PeriodicalId":50574,"journal":{"name":"Discrete & Computational Geometry","volume":"1 1","pages":"1-15"},"PeriodicalIF":0.8,"publicationDate":"2022-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47294246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The εdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$varepsilon $$end{document}-t-Net Problem","authors":"N. Alon, Bruno Jartoux, Chaya Keller, Shakhar Smorodinsky, Yelena Yuditsky","doi":"10.1007/s00454-022-00376-x","DOIUrl":"https://doi.org/10.1007/s00454-022-00376-x","url":null,"abstract":"","PeriodicalId":50574,"journal":{"name":"Discrete & Computational Geometry","volume":"63 1","pages":"618 - 644"},"PeriodicalIF":0.8,"publicationDate":"2022-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90707972","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Three-Dimensional Graph Products with Unbounded Stack-Number","authors":"D. Eppstein, Robert Hickingbotham, Laura Merker, S. Norin, M. Seweryn, D. Wood","doi":"10.1007/s00454-022-00478-6","DOIUrl":"https://doi.org/10.1007/s00454-022-00478-6","url":null,"abstract":"","PeriodicalId":50574,"journal":{"name":"Discrete & Computational Geometry","volume":"1 1","pages":"1-28"},"PeriodicalIF":0.8,"publicationDate":"2022-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44734575","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Density of Binary Disc Packings: The Nine Compact Packings","authors":"Nicolas Bédaride, Thomas Fernique","doi":"10.1007/s00454-021-00348-7","DOIUrl":"https://doi.org/10.1007/s00454-021-00348-7","url":null,"abstract":"","PeriodicalId":50574,"journal":{"name":"Discrete & Computational Geometry","volume":"67 1","pages":"787 - 810"},"PeriodicalIF":0.8,"publicationDate":"2022-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48335465","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Tight Analysis of Geometric Local Search","authors":"Bruno Jartoux, Nabil H. Mustafa","doi":"10.1007/s00454-021-00343-y","DOIUrl":"https://doi.org/10.1007/s00454-021-00343-y","url":null,"abstract":"","PeriodicalId":50574,"journal":{"name":"Discrete & Computational Geometry","volume":"67 1","pages":"361 - 379"},"PeriodicalIF":0.8,"publicationDate":"2022-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45014616","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"In Search of Hyperpaths","authors":"Amir Dahari, N. Linial","doi":"10.1007/s00454-021-00360-x","DOIUrl":"https://doi.org/10.1007/s00454-021-00360-x","url":null,"abstract":"","PeriodicalId":50574,"journal":{"name":"Discrete & Computational Geometry","volume":"69 1","pages":"399-421"},"PeriodicalIF":0.8,"publicationDate":"2022-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48054946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Two Remarks on Graph Norms.","authors":"Frederik Garbe,&nbsp;Jan Hladký,&nbsp;Joonkyung Lee","doi":"10.1007/s00454-021-00280-w","DOIUrl":"https://doi.org/10.1007/s00454-021-00280-w","url":null,"abstract":"<p><p>For a graph <i>H</i>, its homomorphism density in graphs naturally extends to the space of two-variable symmetric functions <i>W</i> in <math><msup><mi>L</mi> <mi>p</mi></msup> </math> , <math><mrow><mi>p</mi> <mo>≥</mo> <mi>e</mi> <mo>(</mo> <mi>H</mi> <mo>)</mo></mrow> </math> , denoted by <i>t</i>(<i>H</i>, <i>W</i>). One may then define corresponding functionals <math> <mrow> <msub><mrow><mo>‖</mo> <mi>W</mi> <mo>‖</mo></mrow> <mi>H</mi></msub> <mspace></mspace> <mo>:</mo> <mo>=</mo> <mspace></mspace> <msup><mrow><mo>|</mo> <mi>t</mi> <mrow><mo>(</mo> <mi>H</mi> <mo>,</mo> <mi>W</mi> <mo>)</mo></mrow> <mo>|</mo></mrow> <mrow><mn>1</mn> <mo>/</mo> <mi>e</mi> <mo>(</mo> <mi>H</mi> <mo>)</mo></mrow> </msup> </mrow> </math> and <math> <mrow> <msub><mrow><mo>‖</mo> <mi>W</mi> <mo>‖</mo></mrow> <mrow><mi>r</mi> <mo>(</mo> <mi>H</mi> <mo>)</mo></mrow> </msub> <mspace></mspace> <mo>:</mo> <mo>=</mo> <mspace></mspace> <mi>t</mi> <msup><mrow><mo>(</mo> <mi>H</mi> <mo>,</mo> <mo>|</mo> <mi>W</mi> <mo>|</mo> <mo>)</mo></mrow> <mrow><mn>1</mn> <mo>/</mo> <mi>e</mi> <mo>(</mo> <mi>H</mi> <mo>)</mo></mrow> </msup> </mrow> </math> , and say that <i>H</i> is (semi-)norming if <math> <msub><mrow><mo>‖</mo> <mspace></mspace> <mo>·</mo> <mspace></mspace> <mo>‖</mo></mrow> <mi>H</mi></msub> </math> is a (semi-)norm and that <i>H</i> is weakly norming if <math> <msub><mrow><mo>‖</mo> <mspace></mspace> <mo>·</mo> <mspace></mspace> <mo>‖</mo></mrow> <mrow><mi>r</mi> <mo>(</mo> <mi>H</mi> <mo>)</mo></mrow> </msub> </math> is a norm. We obtain two results that contribute to the theory of (weakly) norming graphs. Firstly, answering a question of Hatami, who estimated the modulus of convexity and smoothness of <math> <msub><mrow><mo>‖</mo> <mspace></mspace> <mo>·</mo> <mspace></mspace> <mo>‖</mo></mrow> <mi>H</mi></msub> </math> , we prove that <math> <msub><mrow><mo>‖</mo> <mspace></mspace> <mo>·</mo> <mspace></mspace> <mo>‖</mo></mrow> <mrow><mi>r</mi> <mo>(</mo> <mi>H</mi> <mo>)</mo></mrow> </msub> </math> is neither uniformly convex nor uniformly smooth, provided that <i>H</i> is weakly norming. Secondly, we prove that every graph <i>H</i> without isolated vertices is (weakly) norming if and only if each component is an isomorphic copy of a (weakly) norming graph. This strong factorisation result allows us to assume connectivity of <i>H</i> when studying graph norms. In particular, we correct a negligence in the original statement of the aforementioned theorem by Hatami.</p>","PeriodicalId":50574,"journal":{"name":"Discrete & Computational Geometry","volume":"67 3","pages":"919-929"},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00454-021-00280-w","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40308901","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}