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Hadwiger’s conjecture holds for strongly monotypic polytopes 哈德维格猜想对强单型多面体成立
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-09-15 DOI: 10.1007/s00013-025-02170-6
Vuong Bui
{"title":"Hadwiger’s conjecture holds for strongly monotypic polytopes","authors":"Vuong Bui","doi":"10.1007/s00013-025-02170-6","DOIUrl":"10.1007/s00013-025-02170-6","url":null,"abstract":"<div><p>Hadwiger’s conjecture in combinatorial geometry states that any <i>n</i>-dimensional convex body can be covered by at most <span>(2^n)</span> smaller bodies homothetic to the original body. We prove Hadwiger’s conjecture for strongly monotypic polytopes by studying a characterization of the set of normals. One of the nice properties of (strongly) monotypic polytopes is that the set of normals decides the combinatorics of the polytope.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 5","pages":"561 - 568"},"PeriodicalIF":0.5,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145242620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Ma–Qiu index, presentation distance, and local moves in knot theory 结点理论中的马丘指数、表示距离和局部移动
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-09-11 DOI: 10.1007/s00013-025-02168-0
Tetsuya Ito
{"title":"Ma–Qiu index, presentation distance, and local moves in knot theory","authors":"Tetsuya Ito","doi":"10.1007/s00013-025-02168-0","DOIUrl":"10.1007/s00013-025-02168-0","url":null,"abstract":"<div><p>The Ma–Qiu index of a group is the minimum number of normal generators of the commutator subgroup. We show that the Ma–Qiu index gives a lower bound of the presentation distance of two groups, the minimum number of relator replacements to change one group to the other. Since many local moves in knot theory induce relator replacements in knot groups, this shows that the Ma–Qiu index of knot groups gives a lower bound of the Gordian distance based on various local moves. In particular, this gives a unified and simple proof of the Nakanishi index bounds of various unknotting numbers, including virtual or welded knot cases.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 5","pages":"481 - 489"},"PeriodicalIF":0.5,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145242686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the orbits of a finite solvable primitive linear group 有限可解原始线性群的轨道
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-09-08 DOI: 10.1007/s00013-025-02163-5
Mengxi You, Yong Yang
{"title":"On the orbits of a finite solvable primitive linear group","authors":"Mengxi You,&nbsp;Yong Yang","doi":"10.1007/s00013-025-02163-5","DOIUrl":"10.1007/s00013-025-02163-5","url":null,"abstract":"<div><p>In this paper, we strengthen a result of Seager regarding the number of orbits of a solvable primitive linear group.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 5","pages":"455 - 461"},"PeriodicalIF":0.5,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-025-02163-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145242653","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Anisotropic Gohberg lemmas for pseudodifferential operators on Abelian compact groups 阿贝尔紧群上伪微分算子的各向异性Gohberg引理
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-09-06 DOI: 10.1007/s00013-025-02160-8
Marius Măntoiu
{"title":"Anisotropic Gohberg lemmas for pseudodifferential operators on Abelian compact groups","authors":"Marius Măntoiu","doi":"10.1007/s00013-025-02160-8","DOIUrl":"10.1007/s00013-025-02160-8","url":null,"abstract":"<div><p>Classically, Gohberg-type lemmas provide lower bounds for the distance of suitable pseudodifferential operators acting in a Hilbert space to the ideal of compact operators, in terms of “the behavior of the symbol at infinity”. In this article, the pseudodifferential operators are associated to a compact Abelian group <span>(textsf{X})</span> and an important role is played by its Pontryagin dual <span>({widehat{textsf{X}}})</span> . Hörmander-type classes of symbols are not always available; they will be replaced by crossed product <span>(C^*)</span>-algebras involving a vanishing oscillation condition, which anyway is more general even in the particular cases allowing a full pseudodifferential calculus. In addition, the distance to a large class of operator ideals is controlled; the compact operators only form a particular case. This involves invariant closed subsets of certain compactifications of the dual group or, equivalently, invariant ideals of <span>(ell ^infty ({widehat{textsf{X}}}))</span> .</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 4","pages":"399 - 411"},"PeriodicalIF":0.5,"publicationDate":"2025-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037026","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Computing algebraic Belyi functions on Bring’s curve 在Bring曲线上计算代数Belyi函数
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-09-05 DOI: 10.1007/s00013-025-02174-2
Madoka Horie, Takuya Yamauchi
{"title":"Computing algebraic Belyi functions on Bring’s curve","authors":"Madoka Horie,&nbsp;Takuya Yamauchi","doi":"10.1007/s00013-025-02174-2","DOIUrl":"10.1007/s00013-025-02174-2","url":null,"abstract":"<div><p>In this paper, we explicitly compute two kinds of algebraic Belyi functions on Bring’s curve. One is related to a congruence subgroup of <span>(textrm{SL}_2({mathbb {Z}}))</span> and the other is related to a congruence subgroup of the triangle group <span>(Delta (2,4,5)subset textrm{SL}_2({mathbb {R}}).)</span> To carry out the computation, we use elliptic cusp forms of weight 2 for the former case and the automorphism group of Bring’s curve for the latter case. We also discuss a suitable base field (a number field) for describing isomorphisms between Hulek–Craig’s curve, Bring’s curve, and another algebraic model obtained as a modular curve.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 5","pages":"469 - 480"},"PeriodicalIF":0.5,"publicationDate":"2025-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145242685","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
(L^p) boundedness of the Berezin transform on fat Hartogs triangles (L^p) 胖Hartogs三角形上Berezin变换的有界性
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-09-04 DOI: 10.1007/s00013-025-02176-0
Xinchen Wei
{"title":"(L^p) boundedness of the Berezin transform on fat Hartogs triangles","authors":"Xinchen Wei","doi":"10.1007/s00013-025-02176-0","DOIUrl":"10.1007/s00013-025-02176-0","url":null,"abstract":"<div><p>In this paper, we obtain the <span>(L^p)</span> boundedness of the Berezin transform on fat Hartogs triangles for a restricted range of <i>p</i>, which is proved to be sharp.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 5","pages":"513 - 520"},"PeriodicalIF":0.5,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145242684","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Unbounded solutions for Dirichlet problems with degenerate coercivity and a quadratic gradient term 具有退化矫顽力和二次梯度项的Dirichlet问题的无界解
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-09-01 DOI: 10.1007/s00013-025-02151-9
Lucio Boccardo, Andrea Dall’Aglio
{"title":"Unbounded solutions for Dirichlet problems with degenerate coercivity and a quadratic gradient term","authors":"Lucio Boccardo,&nbsp;Andrea Dall’Aglio","doi":"10.1007/s00013-025-02151-9","DOIUrl":"10.1007/s00013-025-02151-9","url":null,"abstract":"<div><p>We give existence results for weak (possibly unbounded) solutions of Dirichlet problems for elliptic equations having degenerate coercivity and a first order term which has quadratic growth with respect to the gradient. The proof is based on the use of test functions having exponential growth.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 3","pages":"323 - 337"},"PeriodicalIF":0.5,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-025-02151-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145011551","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Another character theoretic formula for base size 另一个基本尺寸的字符理论公式
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-08-19 DOI: 10.1007/s00013-025-02165-3
Coen del Valle
{"title":"Another character theoretic formula for base size","authors":"Coen del Valle","doi":"10.1007/s00013-025-02165-3","DOIUrl":"10.1007/s00013-025-02165-3","url":null,"abstract":"<div><p>A base for a permutation group <i>G</i> acting on a set <span>(Omega )</span> is a sequence <span>(mathcal {B})</span> of points of <span>(Omega )</span> such that the pointwise stabiliser <span>(G_{mathcal {B}})</span> is trivial. The base size of <i>G</i> is the size of a smallest base for <i>G</i>. Extending the results of a recent paper of the author, we prove a 2013 conjecture of Fritzsche, Külshammer, and Reiche. Moreover, we generalise this conjecture and derive an alternative character theoretic formula for the base size of a certain class of permutation groups. As a consequence of our work, a third formula for the base size of the symmetric group of degree <i>n</i> acting on the subsets of <span>({1,2,dots , n})</span> is obtained.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 5","pages":"463 - 468"},"PeriodicalIF":0.5,"publicationDate":"2025-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-025-02165-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145242682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Uniformity in the Fourier inversion formula with applications to Laplace transforms 傅里叶反变换公式的均匀性及其在拉普拉斯变换中的应用
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-08-16 DOI: 10.1007/s00013-025-02153-7
Joannis Alexopoulos
{"title":"Uniformity in the Fourier inversion formula with applications to Laplace transforms","authors":"Joannis Alexopoulos","doi":"10.1007/s00013-025-02153-7","DOIUrl":"10.1007/s00013-025-02153-7","url":null,"abstract":"<div><p>We systematically find conditions which yield locally uniform convergence in the Fourier inversion formula in one and higher dimensions. We apply the gained knowledge to the complex inversion formula of the Laplace transform to extend known results for Banach space-valued functions and, specifically, for <span>(C_0)</span>-semigroups.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 4","pages":"413 - 432"},"PeriodicalIF":0.5,"publicationDate":"2025-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-025-02153-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037040","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Relative Gromov–Witten and maximal contact conics 相对Gromov-Witten和最大接触二次曲线
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2025-08-16 DOI: 10.1007/s00013-025-02169-z
Giosuè Muratore
{"title":"Relative Gromov–Witten and maximal contact conics","authors":"Giosuè Muratore","doi":"10.1007/s00013-025-02169-z","DOIUrl":"10.1007/s00013-025-02169-z","url":null,"abstract":"<div><p>We discuss some properties of the relative Gromov–Witten invariants counting rational curves with maximal contact order at one point. We compute the number of Cayley’s sextactic conics to any smooth plane curve. In particular, we compute the contribution, from double covers of inflectional lines, to a certain degree two relative Gromov–Witten invariant relative to the curve.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"125 5","pages":"491 - 503"},"PeriodicalIF":0.5,"publicationDate":"2025-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145242683","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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