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Asymptotics of the shifted finite differences of the overpartition function and a problem of Wang–Xie–Zhang 过配分函数的位移有限差分的渐近性及王协章问题
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-03-17 DOI: 10.1007/s00013-025-02219-6
Gargi Mukherjee
{"title":"Asymptotics of the shifted finite differences of the overpartition function and a problem of Wang–Xie–Zhang","authors":"Gargi Mukherjee","doi":"10.1007/s00013-025-02219-6","DOIUrl":"10.1007/s00013-025-02219-6","url":null,"abstract":"<div><p>Let <span>(overline{p}(n))</span> denote the overpartition function, and for <span>(jin mathbb {N})</span>, <span>(Delta ^r_j)</span> denote the <i>r</i>-fold applications of the shifted difference operator <span>(Delta _j)</span> defined by <span>(Delta _j(a)(n):=a(n)-a(n-j))</span>. The main goal of this paper is to derive an asymptotic expansion of <span>(Delta ^r_j(overline{p})(n))</span> with an effective error bound which subsequently gives an answer to a problem of Wang, Xie, and Zhang. In order to get the asymptotics of <span>(Delta ^r_j(overline{p})(n))</span>, we derive an asymptotic expansion of the shifted overpartition function <span>(overline{p}(n+k))</span> for any integer <span>(kne 0)</span>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 4","pages":"383 - 396"},"PeriodicalIF":0.5,"publicationDate":"2026-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147636893","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
A comparison of the regularity of certain classes of monomial ideals and their integral closure 单项式理想若干类的正则性及其整体闭包的比较
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-03-14 DOI: 10.1007/s00013-026-02225-2
Omkar Javadekar
{"title":"A comparison of the regularity of certain classes of monomial ideals and their integral closure","authors":"Omkar Javadekar","doi":"10.1007/s00013-026-02225-2","DOIUrl":"10.1007/s00013-026-02225-2","url":null,"abstract":"<div><p>Let <span>(S = textsf{k}[x_1, ldots , x_n])</span>, <i>I</i> be an ideal of <i>S</i>, and <span>(bar{I})</span> denote its integral closure. A conjecture of Küronya and Pintye states that for any homogeneous ideal <i>I</i> of <i>S</i>, the inequality <span>(operatorname {reg}(bar{I}) le operatorname {reg}(I))</span> holds, where <span>(operatorname {reg}(_))</span> denotes the Castelnuovo–Mumford regularity. In this article, we prove the conjecture for certain classes of monomial ideals.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 4","pages":"351 - 363"},"PeriodicalIF":0.5,"publicationDate":"2026-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147636891","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
Sharp bounds for the growth and distortion of the analytic part of convex K-quasiconformal harmonic mappings 凸k -拟共形调和映射解析部分的生长和畸变的尖锐界
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-03-14 DOI: 10.1007/s00013-026-02227-0
Peijin Li, Saminathan Ponnusamy
{"title":"Sharp bounds for the growth and distortion of the analytic part of convex K-quasiconformal harmonic mappings","authors":"Peijin Li,&nbsp;Saminathan Ponnusamy","doi":"10.1007/s00013-026-02227-0","DOIUrl":"10.1007/s00013-026-02227-0","url":null,"abstract":"<div><p>The main aim of this paper is to obtain the sharp upper and lower bounds for the growth and distortion of the analytic part <i>h</i> of sense-preserving convex <i>K</i>-quasiconformal harmonic mappings.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 4","pages":"407 - 416"},"PeriodicalIF":0.5,"publicationDate":"2026-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147636859","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
(pmb {partial bar{partial }})-Lemma and Steinness for Riemann domains over Stein manifolds (pmb {partial bar{partial }})- Stein流形上Riemann域的引理和Steinness
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-03-09 DOI: 10.1007/s00013-026-02232-3
Shun Sugiyama
{"title":"(pmb {partial bar{partial }})-Lemma and Steinness for Riemann domains over Stein manifolds","authors":"Shun Sugiyama","doi":"10.1007/s00013-026-02232-3","DOIUrl":"10.1007/s00013-026-02232-3","url":null,"abstract":"<div><p>Let <span>((D,pi ))</span> be a connected Riemann domain over an <i>n</i>-dimensional Stein manifold which satisfies <span>(H_1(D,{mathbb {Z}})=0)</span> and <span>(H^k(D,{mathscr {O}})=0)</span> for <span>(2le kle n-1.)</span> Then <span>((D,pi ))</span> is Stein if and only if <span>((D,pi ))</span> satisfies the <span>(partial bar{partial })</span>-lemma.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 5","pages":"501 - 504"},"PeriodicalIF":0.5,"publicationDate":"2026-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147967920","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
Double ergodicity of strong horseshoe maps 强马蹄形地图的双遍历性
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-03-06 DOI: 10.1007/s00013-026-02221-6
Aliasghar Sarizadeh
{"title":"Double ergodicity of strong horseshoe maps","authors":"Aliasghar Sarizadeh","doi":"10.1007/s00013-026-02221-6","DOIUrl":"10.1007/s00013-026-02221-6","url":null,"abstract":"<div><p>In this paper, we investigate the double ergodicity of strong horseshoe maps, defined as onto maps whose phase spaces act as attractors for their inverse iterations. We prove that such maps, when possessing the reverse bounded distortion property, are doubly ergodic with respect to the Lebesgue measure. Additionally, we establish the robustness of double ergodicity and weak mixing for a <span>(C^1)</span>-perturbed doubling map on the circle, demonstrating that all maps in a <span>(C^1)</span>-neighborhood, as given in Theorem B, share these properties.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 4","pages":"425 - 431"},"PeriodicalIF":0.5,"publicationDate":"2026-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147636894","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
Non-solutions to mixed equations in acylindrically hyperbolic groups coming from random walks 随机漫步的非圆柱形双曲群混合方程的非解
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-03-03 DOI: 10.1007/s00013-026-02223-4
Henry Bradford, Alessandro Sisto
{"title":"Non-solutions to mixed equations in acylindrically hyperbolic groups coming from random walks","authors":"Henry Bradford,&nbsp;Alessandro Sisto","doi":"10.1007/s00013-026-02223-4","DOIUrl":"10.1007/s00013-026-02223-4","url":null,"abstract":"<div><p>A mixed equation in a group <i>G</i> is given by a non-trivial element <i>w</i>(<i>x</i>) of the free product <span>(G *mathbb {Z})</span>, and a solution is some <span>(gin G)</span> such that <i>w</i>(<i>g</i>) is the identity. For <i>G</i> acylindrically hyperbolic with trivial finite radical (e.g. torsion-free), we show that any mixed equation of length <i>n</i> has a non-solution of length comparable to <span>(log (n))</span>, which is the best possible bound. Similarly, we show that there is a common non-solution of length <i>O</i>(<i>n</i>) to all mixed equations of length <i>n</i>, again the best possible bound. In fact, in both cases, we show that a random walk of appropriate length yields a non-solution with positive probability.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 4","pages":"343 - 350"},"PeriodicalIF":0.5,"publicationDate":"2026-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-026-02223-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147636861","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
On adjoint orbits in nilpotent ideals of a Borel subalgebra Borel子代数的幂零理想中的伴随轨道
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-02-09 DOI: 10.1007/s00013-025-02218-7
Rupert W. T. Yu
{"title":"On adjoint orbits in nilpotent ideals of a Borel subalgebra","authors":"Rupert W. T. Yu","doi":"10.1007/s00013-025-02218-7","DOIUrl":"10.1007/s00013-025-02218-7","url":null,"abstract":"<div><p>Let <span>(mathfrak {m})</span> be a nilpotent ideal in the Borel subalgebra <span>(mathfrak {b})</span> of a complex finite-dimensional semisimple Lie algebra, and <span>(mathfrak {m}^{bullet })</span> the subset of (ad-)nilpotent elements in <span>(mathfrak {b})</span> such that <span>(mathfrak {m})</span> is the minimal ideal containing them. This set is stable under the adjoint action of the corresponding Borel subgroup <span>(textbf{B})</span>. We prove that <span>(mathfrak {m}^{bullet })</span> contains a unique closed <span>(textbf{B})</span>-orbit which is the orbit of a nilpotent element whose support is the set of minimal roots associated to the root space decomposition of <span>(mathfrak {m})</span>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 4","pages":"365 - 375"},"PeriodicalIF":0.5,"publicationDate":"2026-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147636862","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
A note on involution prefixes in Coxeter groups 考克斯特群中对合前缀的注释
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-02-07 DOI: 10.1007/s00013-025-02220-z
Sarah B. Hart, Peter J. Rowley
{"title":"A note on involution prefixes in Coxeter groups","authors":"Sarah B. Hart,&nbsp;Peter J. Rowley","doi":"10.1007/s00013-025-02220-z","DOIUrl":"10.1007/s00013-025-02220-z","url":null,"abstract":"<div><p>Let (<i>W</i>, <i>R</i>) be a Coxeter system and let <span>(w in W)</span>. We say that <i>u</i> is a <i>prefix</i> of <i>w</i> if there is a reduced expression for <i>u</i> that can be extended to one for <i>w</i>. That is, <span>(w = uv)</span> for some <i>v</i> in <i>W</i> such that <span>(ell (w) = ell (u) + ell (v))</span>. We say that <i>w</i> has the <i>ancestor property</i> if the set of prefixes of <i>w</i> contains a unique involution of maximal length. In this paper, we show that all Coxeter elements of finitely generated Coxeter groups have the ancestor property, and hence a canonical expression as a product of involutions. We conjecture that the property in fact holds for all non-identity elements of finite Coxeter groups.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 3","pages":"231 - 237"},"PeriodicalIF":0.5,"publicationDate":"2026-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147337472","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
Spectrally additive maps on the positive cones of the Wiener algebra 维纳代数正锥上的谱加性映射
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-02-07 DOI: 10.1007/s00013-026-02224-3
Shiho Oi, Kaito Sato
{"title":"Spectrally additive maps on the positive cones of the Wiener algebra","authors":"Shiho Oi,&nbsp;Kaito Sato","doi":"10.1007/s00013-026-02224-3","DOIUrl":"10.1007/s00013-026-02224-3","url":null,"abstract":"<div><p>We study surjective maps between the positive cones of the Wiener algebra that preserve the spectrum of the sum of every two elements. We show that such maps can be extended to isometric real-linear isomorphisms of the Wiener algebra.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 4","pages":"417 - 423"},"PeriodicalIF":0.5,"publicationDate":"2026-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147636860","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
Medial axis detects non-Lipschitz normally embedded points 内轴检测非lipschitz正常嵌入点
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-02-07 DOI: 10.1007/s00013-025-02216-9
Adam Białożyt
{"title":"Medial axis detects non-Lipschitz normally embedded points","authors":"Adam Białożyt","doi":"10.1007/s00013-025-02216-9","DOIUrl":"10.1007/s00013-025-02216-9","url":null,"abstract":"<div><p>We show that the (multi)function of the closest points is locally Lipschitz outside of the medial axis of a closed set <span>(Xsubset mathbb {R}^n)</span>. With this result, we prove that the medial axis of <i>X</i> approaches every point where <i>X</i> is not Lipschitz normally embedded.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 3","pages":"285 - 293"},"PeriodicalIF":0.5,"publicationDate":"2026-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-025-02216-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147337471","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
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