数学最新文献

{"title":"Generator polynomial matrices of the Galois hulls of multi-twisted codes","authors":"Ramy Taki Eldin ,&nbsp;Patrick Solé","doi":"10.1016/j.ffa.2025.102712","DOIUrl":"10.1016/j.ffa.2025.102712","url":null,"abstract":"<div><div>In this study, we consider the Euclidean and Galois hulls of multi-twisted (MT) codes over a finite field <span><math><msub><mrow><mi>F</mi></mrow><mrow><msup><mrow><mi>p</mi></mrow><mrow><mi>e</mi></mrow></msup></mrow></msub></math></span> of characteristic <em>p</em>. Let <strong>G</strong> be a generator polynomial matrix (GPM) of an MT code <span><math><mi>C</mi></math></span>. For any <span><math><mn>0</mn><mo>≤</mo><mi>κ</mi><mo>&lt;</mo><mi>e</mi></math></span>, the <em>κ</em>-Galois hull of <span><math><mi>C</mi></math></span>, denoted by <span><math><msub><mrow><mi>h</mi></mrow><mrow><mi>κ</mi></mrow></msub><mrow><mo>(</mo><mi>C</mi><mo>)</mo></mrow></math></span>, is the intersection of <span><math><mi>C</mi></math></span> with its <em>κ</em>-Galois dual. The main result in this paper is that a GPM for <span><math><msub><mrow><mi>h</mi></mrow><mrow><mi>κ</mi></mrow></msub><mrow><mo>(</mo><mi>C</mi><mo>)</mo></mrow></math></span> has been obtained from <strong>G</strong>. We start by associating a linear code <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mi>G</mi></mrow></msub></math></span> with <strong>G</strong>. We show that <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mi>G</mi></mrow></msub></math></span> is quasi-cyclic. In addition, we prove that the dimension of <span><math><msub><mrow><mi>h</mi></mrow><mrow><mi>κ</mi></mrow></msub><mrow><mo>(</mo><mi>C</mi><mo>)</mo></mrow></math></span> is the difference between the dimension of <span><math><mi>C</mi></math></span> and that of <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mi>G</mi></mrow></msub></math></span>. Thus the determinantal divisors are used to derive a formula for the dimension of <span><math><msub><mrow><mi>h</mi></mrow><mrow><mi>κ</mi></mrow></msub><mrow><mo>(</mo><mi>C</mi><mo>)</mo></mrow></math></span>. Finally, we deduce a GPM formula for <span><math><msub><mrow><mi>h</mi></mrow><mrow><mi>κ</mi></mrow></msub><mrow><mo>(</mo><mi>C</mi><mo>)</mo></mrow></math></span>. In particular, we handle the cases of <em>κ</em>-Galois self-orthogonal and linear complementary dual MT codes; we establish equivalent conditions that characterize these cases. Equivalent results can be deduced immediately for the classes of cyclic, constacyclic, quasi-cyclic, generalized quasi-cyclic, and quasi-twisted codes, because they are all special cases of MT codes. Some numerical examples, containing codes with the best-known parameters, are used to illustrate the theoretical results.</div></div>","PeriodicalId":50446,"journal":{"name":"Finite Fields and Their Applications","volume":"109 ","pages":"Article 102712"},"PeriodicalIF":1.2,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144772334","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":"Stability in Bondy's theorem on paths and cycles","authors":"Bo Ning ,&nbsp;Long-Tu Yuan","doi":"10.1016/j.jctb.2025.07.004","DOIUrl":"10.1016/j.jctb.2025.07.004","url":null,"abstract":"<div><div>In this paper, we study the stability result of a well-known theorem of Bondy. We prove that for any 2-connected non-hamiltonian graph, if every vertex except for at most one vertex has degree at least <em>k</em>, then it contains a cycle of length at least <span><math><mn>2</mn><mi>k</mi><mo>+</mo><mn>2</mn></math></span> except for some special families of graphs. Our results imply several previous classical theorems including a deep and old result by Voss. We point out our result on stability in Bondy's theorem can directly imply a positive solution (in a slight stronger form) to the following problem: Is there a polynomial time algorithm to decide whether a 2-connected graph <em>G</em> on <em>n</em> vertices has a cycle of length at least <span><math><mi>min</mi><mo>⁡</mo><mo>{</mo><mn>2</mn><mi>δ</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>+</mo><mn>2</mn><mo>,</mo><mi>n</mi><mo>}</mo></math></span>? This problem originally motivates the recent study on algorithmic aspects of Dirac's theorem by Fomin, Golovach, Sagunov, and Simonov, although a stronger problem was solved by them by completely different methods. Our theorem can also help us to determine all extremal graphs for wheels on odd number of vertices. We also discuss the relationship between our results and some previous problems and theorems in spectral graph theory and generalized Turán problems.</div></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"175 ","pages":"Pages 213-239"},"PeriodicalIF":1.2,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144772391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Regularity and convergence of critical points of an Ambrosio-Tortorelli functional with linear growth and of its Γ-limit","authors":"Rebecca Continolo,&nbsp;Virginia Lorenzini,&nbsp;Riccardo Scala,&nbsp;Giuseppe Scianna","doi":"10.1016/j.jde.2025.113654","DOIUrl":"10.1016/j.jde.2025.113654","url":null,"abstract":"<div><div>In the one-dimensional setting we consider an Ambrosio-Tortorelli functional <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>ε</mi></mrow></msub><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></math></span> which has linear growth with respect to <span><math><msup><mrow><mi>u</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span>. We prove that under suitable conditions on the fidelity term, minimizers and critical points of <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>ε</mi></mrow></msub></math></span> are Sobolev regular, and that the same is true for the Γ-limit <em>F</em> of <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>ε</mi></mrow></msub></math></span>. As a corollary, we obtain that the functional <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>w</mi></mrow></msub><mo>(</mo><mi>u</mi><mo>)</mo></math></span> computing the length of the generalized graph of a function of bounded variation <em>u</em>, under the same conditions on the fidelity term, admits a unique minimizer of class <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>. This partially solves a conjecture by De Giorgi <span><span>[16]</span></span> in the one-dimensional case.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"445 ","pages":"Article 113654"},"PeriodicalIF":2.3,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144766663","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Brunn-Minkowski and reverse isoperimetric inequalities for dual quermassintegrals","authors":"Shay Sadovsky,&nbsp;Gaoyong Zhang","doi":"10.1016/j.aim.2025.110456","DOIUrl":"10.1016/j.aim.2025.110456","url":null,"abstract":"<div><div>This paper establishes two new geometric inequalities in the dual Brunn-Minkowski theory. The first, originally conjectured by Lutwak, is the Brunn-Minkowski inequality for dual quermassintegrals of origin-symmetric convex bodies. The second, generalizing Ball's volume ratio inequality, is a reverse isoperimetric inequality: among all origin-symmetric convex bodies in John's position, the cube maximizes the dual quermassintegrals.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"480 ","pages":"Article 110456"},"PeriodicalIF":1.5,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144767100","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On Bekollé-Bonami weights in general domains in Rn","authors":"María José González ,&nbsp;José G. Llorente","doi":"10.1016/j.jmaa.2025.129946","DOIUrl":"10.1016/j.jmaa.2025.129946","url":null,"abstract":"<div><div>The purpose of this note is to extend the definition of Bekollé-Bonami weights to domains in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>,</mo><mspace></mspace><mi>n</mi><mo>≥</mo><mn>2</mn></math></span>, investigate their properties and establish Carleson-type embedding theorems analogous to the ones existing in the classical setting. It turns out that, in this context, the geometry of the domain plays a decisive role.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"554 1","pages":"Article 129946"},"PeriodicalIF":1.2,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144771804","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":"Rescaled Bayes factors: A class of e-variables","authors":"Thorsten Dickhaus","doi":"10.1016/j.spl.2025.110511","DOIUrl":"10.1016/j.spl.2025.110511","url":null,"abstract":"<div><div>A class of e-variables is introduced and analyzed. Some examples are presented.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"226 ","pages":"Article 110511"},"PeriodicalIF":0.7,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144770952","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}

{"title":"Contractions in perfect graphs","authors":"Alexandre Dupont-Bouillard ,&nbsp;Pierre Fouilhoux ,&nbsp;Roland Grappe ,&nbsp;Mathieu Lacroix","doi":"10.1016/j.dam.2025.07.022","DOIUrl":"10.1016/j.dam.2025.07.022","url":null,"abstract":"<div><div>In this paper, we characterize in several manners the class of <em>contraction perfect</em> graphs which are the perfect graphs that remain perfect after the contraction of any edge set. We define the utter graph <span><math><mrow><mi>u</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> which is the graph whose stable sets are in bijection with the co-2-plexes of <span><math><mi>G</mi></math></span>, and prove that <span><math><mrow><mi>u</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> is perfect if and only if <span><math><mi>G</mi></math></span> is contraction perfect. Moreover, we exhibit the strong link between co-2-plexes and induced matchings and discuss its consequences according to known results on these problems. This yields several classes of graphs for which the maximum weighted co-2-plex is solvable in polynomial time. Finally, we show how our results extend to a new class of graphs for which finding a maximum weighted induced matching can be done in polynomial time.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"377 ","pages":"Pages 380-389"},"PeriodicalIF":1.0,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144766977","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":"Which Laplacian cospectral graphs have the same degree sequences?","authors":"Qianlin Yao ,&nbsp;Yuling Lan ,&nbsp;Jiachang Ye ,&nbsp;Haiying Shan","doi":"10.1016/j.disc.2025.114720","DOIUrl":"10.1016/j.disc.2025.114720","url":null,"abstract":"<div><div>Liu et al. (2018) <span><span>[13]</span></span> raised the problem: “Which cospectral graphs have the same degree sequences?”. In this paper, we introduce some graph operations affecting the Laplacian spectral radius of a graph, and then provide a new method to construct Laplacian cospectral graphs from old Laplacian cospectral graphs. Based on this, we show that: Let <em>G</em> be a connected graph and let <em>H</em> be Laplacian cospectral with <em>G</em>. If the second largest Laplacian eigenvalue of graph <em>G</em> is less than 4, and <em>G</em> and <em>H</em> are not spanning subgraphs of <span><math><msub><mrow><mi>W</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>, then <em>H</em> must have the same degree sequence as <em>G</em>, where <span><math><msub><mrow><mi>W</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> is a specific graph defined in the paper. This result extends the corresponding result of Liu et al. (2018) <span><span>[13]</span></span>. Besides, extremal graphs are also provided to show that the condition related to <span><math><msub><mrow><mi>W</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> is crucial.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"349 2","pages":"Article 114720"},"PeriodicalIF":0.7,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144767050","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":"Babai numbers and Babai spectra of paths and cycles","authors":"Peter Johnson ,&nbsp;Celalettin Kaya ,&nbsp;Ryan W. Matzke","doi":"10.1016/j.disc.2025.114721","DOIUrl":"10.1016/j.disc.2025.114721","url":null,"abstract":"<div><div>We study Babai numbers and Babai <em>k</em>-spectra of paths and cycles. We completely determine the Babai numbers of paths <span><math><msub><mrow><mi>P</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> for <span><math><mi>n</mi><mo>&gt;</mo><mn>1</mn></math></span> and <span><math><mn>1</mn><mo>≤</mo><mi>k</mi><mo>≤</mo><mi>n</mi><mo>−</mo><mn>1</mn></math></span>, and the Babai <em>k</em>-spectra for <span><math><msub><mrow><mi>P</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> when <span><math><mn>1</mn><mo>≤</mo><mi>k</mi><mo>≤</mo><mi>n</mi><mo>/</mo><mn>2</mn></math></span>. We also completely determine Babai numbers and Babai <em>k</em>-spectra of all cycles <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> for <span><math><mi>k</mi><mo>∈</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo></math></span> and <span><math><mi>n</mi><mo>≥</mo><mn>3</mn></math></span> if <span><math><mi>k</mi><mo>=</mo><mn>1</mn></math></span> and <span><math><mi>n</mi><mo>&gt;</mo><mn>3</mn></math></span> if <span><math><mi>k</mi><mo>=</mo><mn>2</mn></math></span>.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"349 2","pages":"Article 114721"},"PeriodicalIF":0.7,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144767051","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":"G1 Hermite interpolation by planar quintic-like algebraic–trigonometric Pythagorean-hodograph curves","authors":"Yong-Xia Hao,&nbsp;Di Wu","doi":"10.1016/j.cam.2025.116972","DOIUrl":"10.1016/j.cam.2025.116972","url":null,"abstract":"<div><div>This paper discusses the construction of Algebraic–trigonometric Pythagorean-hodograph (ATPH) quintic-like curves, where the end-points, end-tangents, and a specified arc length are prescribed. Through reduction of the original data to canonical form with equal-magnitude, a comprehensive characterization of the solutions is achieved. This characterization is framed as the task of determining the real solutions to a system of quadratic equations, which incorporates a global free shape parameter <span><math><mi>α</mi></math></span>. After careful analysis, it is demonstrated that the system possesses two closed-form solutions. To facilitate practical implementation, the corresponding algorithm is presented in detail. Furthermore, several illustrative examples are provided to demonstrate the construction process and explore the impact of the shape parameter <span><math><mi>α</mi></math></span> on the ATPH quintic-like curves. These examples not only show the flexibility offered by <span><math><mi>α</mi></math></span>, but also provide valuable insights into how this parameter can be manipulated to achieve desired curve shapes.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"474 ","pages":"Article 116972"},"PeriodicalIF":2.6,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144771271","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}