MathematikaPub Date : 2026-03-25DOI: 10.1112/mtk.70086
Jesús Jerónimo-Castro, Luis Montejano, Efrén Morales-Amaya
{"title":"Flat grazes of convex bodies and local characterization of quadrics","authors":"Jesús Jerónimo-Castro, Luis Montejano, Efrén Morales-Amaya","doi":"10.1112/mtk.70086","DOIUrl":"10.1112/mtk.70086","url":null,"abstract":"<p>We prove several local characterizations of quadrics, among them, the local Blaschke's Theorem, and use this result to give some characterizations of the ellipsoid related to the flatness of its grazes.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"72 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2026-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147569056","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}
MathematikaPub Date : 2026-03-25DOI: 10.1112/mtk.70086
Jesús Jerónimo-Castro, Luis Montejano, Efrén Morales-Amaya
{"title":"Flat grazes of convex bodies and local characterization of quadrics","authors":"Jesús Jerónimo-Castro, Luis Montejano, Efrén Morales-Amaya","doi":"10.1112/mtk.70086","DOIUrl":"https://doi.org/10.1112/mtk.70086","url":null,"abstract":"<p>We prove several local characterizations of quadrics, among them, the local Blaschke's Theorem, and use this result to give some characterizations of the ellipsoid related to the flatness of its grazes.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"72 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2026-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147569252","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}
MathematikaPub Date : 2026-03-20DOI: 10.1112/mtk.70083
Noy Soffer Aranov, Angelot Behajaina
{"title":"Counting problems for orthogonal sets and sublattices in function fields","authors":"Noy Soffer Aranov, Angelot Behajaina","doi":"10.1112/mtk.70083","DOIUrl":"10.1112/mtk.70083","url":null,"abstract":"<p>Let <span></span><math></math>. Analogous to orthogonality in the Euclidean space <span></span><math></math>, there exists a well-studied notion of ultrametric orthogonality in <span></span><math></math>. In this paper, we extend the work of [4] on counting problems related to orthogonality in <span></span><math></math>. For example, we resolve an open question posed in [4] by bounding the size of the largest “orthogonal sets” in <span></span><math></math>. Furthermore, using similar ideas and techniques, we investigate analogues of Hadamard matrices over <span></span><math></math>. Finally, we also use ultrametric orthogonality to compute the number of sublattices of <span></span><math></math> with a certain geometric structure, and to determine the number of orthogonal bases of a sublattice in <span></span><math></math>. The resulting formulas depend crucially on successive minima.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"72 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2026-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.70083","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147567416","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}
MathematikaPub Date : 2026-03-20DOI: 10.1112/mtk.70083
Noy Soffer Aranov, Angelot Behajaina
{"title":"Counting problems for orthogonal sets and sublattices in function fields","authors":"Noy Soffer Aranov, Angelot Behajaina","doi":"10.1112/mtk.70083","DOIUrl":"https://doi.org/10.1112/mtk.70083","url":null,"abstract":"<p>Let <span></span><math></math>. Analogous to orthogonality in the Euclidean space <span></span><math></math>, there exists a well-studied notion of ultrametric orthogonality in <span></span><math></math>. In this paper, we extend the work of [4] on counting problems related to orthogonality in <span></span><math></math>. For example, we resolve an open question posed in [4] by bounding the size of the largest “orthogonal sets” in <span></span><math></math>. Furthermore, using similar ideas and techniques, we investigate analogues of Hadamard matrices over <span></span><math></math>. Finally, we also use ultrametric orthogonality to compute the number of sublattices of <span></span><math></math> with a certain geometric structure, and to determine the number of orthogonal bases of a sublattice in <span></span><math></math>. The resulting formulas depend crucially on successive minima.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"72 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2026-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.70083","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147567264","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}
MathematikaPub Date : 2026-03-19DOI: 10.1112/mtk.70085
Gergely Ambrus, Rainie Heck
{"title":"A note on the Steinitz lemma","authors":"Gergely Ambrus, Rainie Heck","doi":"10.1112/mtk.70085","DOIUrl":"https://doi.org/10.1112/mtk.70085","url":null,"abstract":"<p>We establish the connection between the Steinitz problem for ordering vector families in arbitrary norms and its variant for not necessarily zero-sum families consisting of “nearly unit” vectors.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"72 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2026-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.70085","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147567168","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}