Acta Mathematica Hungarica最新文献

{"title":"On the number of vertices/edges whose deletion preserves the Kőnig–Egerváry property","authors":"V. E. Levit,&nbsp;E. Mandrescu","doi":"10.1007/s10474-025-01549-9","DOIUrl":"10.1007/s10474-025-01549-9","url":null,"abstract":"<div><p>Let <span>(alpha(G))</span>\u0000 and <span>(mu(G))</span>\u0000 denote the cardinality of a maximum independent\u0000set and the size of a maximum matching, respectively, in the graph <span>(G= (V,E) )</span>\u0000. If <span>(alpha(G)+mu(G)= lvert V rvert )</span>\u0000, then <i>G</i> is a\u0000Kőnig–Egerváry graph.</p><p>The number <span>(d (G) =max{ lvert A rvert - lvert N (A) rvert :Asubseteq V})</span> is the critical\u0000difference of the graph <i>G</i>, where <span>(N (A) =left{ v:vin V,N (v) cap Aneqemptysetright} )</span>\u0000. Every set <span>(Bsubseteq V)</span>\u0000satisfying <span>(d (G) = lvert B rvert - lvert N (B) rvert )</span>\u0000 is <i>critical</i>. Let <span>(varepsilon (G) = lvert mathrm{ker}(G) rvert )</span>\u0000 and <span>(xi (G) = lvert mathrm{core} (G) rvert )</span>\u0000, where <span>(mathrm{ker}(G))</span>\u0000 is the intersection of all critical independent sets, and <span>( mathrm{core} (G) )</span>\u0000 is the intersection of all maximum independent sets. It\u0000is known that <span>(mathrm{ker}(G)subseteq)</span>\u0000 <span>( mathrm{core} (G) )</span>\u0000holds for every graph.</p><p>Let us define\u0000</p><ul>\u0000 <li>\u0000 <p><span>(varrho_{v} (G) = lvert { vin V:G-v )</span> is a Kőnig–Egerváry graph <span>(} rvert )</span>;</p>\u0000 </li>\u0000 <li>\u0000 <p><span>(varrho_{e} (G) = lvert { ein E:G-e )</span> is a Kőnig–Egerváry graph <span>( } rvert )</span>.</p>\u0000 </li>\u0000 </ul><p>Clearly, <span>(varrho_{v} (G) = lvert V rvert )</span> and\u0000<span>(varrho_{e} (G) = lvert E rvert )</span> for bipartite graphs.\u0000Unlike the bipartiteness, the property of being a Kőnig–Egerváry graph\u0000is not hereditary.</p><p>In this paper, we show that\u0000</p><div><div><span>$$varrho_{v} (G) = lvert V rvert -xi (G) +varepsilon (G)phantom{a} phantom{a}text{and}phantom{a} phantom{a} varrho_{e} (G) geq lvert E rvert -xi (G) +varepsilon (G)$$</span></div></div><p> for every Kőnig–Egerváry graph <i>G</i>.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"176 2","pages":"321 - 340"},"PeriodicalIF":0.6,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145230540","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 linear independence criterion for certain infinite series with polynomial orders","authors":"S. Kudo","doi":"10.1007/s10474-025-01548-w","DOIUrl":"10.1007/s10474-025-01548-w","url":null,"abstract":"<div><p>Let <i>q</i> be a Pisot or Salem number. Let <span>(f_j(x) quad (j=1,2,dots))</span> be integer-valued polynomials of degree <span>(ge2)</span> with positive leading coefficients, and let <span>({a_j (n)}_{nge1} quad (j=1,2,dots))</span> be sequences of algebraic integers in the field <span>(Q(q))</span> with suitable growth conditions. In this paper, we investigate linear independence over <span>(Q(q))</span> of the numbers</p><div><div><span>$$1,quad sum_{n=1}^{infty} frac{a_j (n)}{q^{f_j (n)}} quad (j=1,2,dots).$$</span></div></div><p> In particular, when <span>(a_j(n) quad (j=1,2,dots))</span> are polynomials of <i>n</i>, we give a linear independence criterion for the above numbers.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"176 2","pages":"341 - 364"},"PeriodicalIF":0.6,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145230533","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":"Constructions on the Poincaré-disk","authors":"D. Veres","doi":"10.1007/s10474-025-01551-1","DOIUrl":"10.1007/s10474-025-01551-1","url":null,"abstract":"<div><p> This paper concerns with implementations of constructions in\u0000the Poincaré model of hyperbolic geometry and their applications to proofs of\u0000selected theorems. The main motivation is how some hyperbolic geometric \u0000statements can be proven using elementary methods within the model. By embedding\u0000hyperbolic geometry into the Euclidean plane, certain proofs can become more\u0000accessible and comprehensible.</p><p>In this paper, we present two elementary constructions developed by using\u0000the Poincaré model, followed by novel-approached answers to the following \u0000questions. Does a common perpendicular always exist for two ultraparallel lines? Can\u0000a given line segment be divided into <span>(n)</span> equal parts? Is it possible to construct a\u0000triangle from three given angles, provided their sum is less than 180 degrees?</p><p>Although there exist known answers to these questions, the usual proofs \u0000involve strong theorems or trigonometric functions requiring extensive calculations\u0000(e.g. [6] and [2]). Instead, hereby we present proofs using elementary tools with\u0000easily understandable steps.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"176 2","pages":"437 - 446"},"PeriodicalIF":0.6,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145230539","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":"New weak Herz spaces with variable exponent and the boundedness of some sublinear operators","authors":"K. Matsuoka","doi":"10.1007/s10474-025-01542-2","DOIUrl":"10.1007/s10474-025-01542-2","url":null,"abstract":"<div><p>In the investigations of the boundedness of some sublinear operators, which do not hold the strong estimates, the researchers treat the weak estimates. In this occasion for the Herz spaces <span>(dot{K}_q^{alpha,p}({mathbb{R}}^n))</span>, in order to obtain more precise estimates \u0000than the weak estimates, the author [40] introduced the new “weak” Herz spaces <span>(widetilde{W}dot{K}_q^{alpha,p}({mathbb{R}}^n))</span> and showed the new “weak” boundedness on <span>(dot{K}_q^{alpha,p}({mathbb{R}}^n))</span>. In this paper, we will extend the above new “weak” estimates to the sublinear operators satisfying another size condition. Further, we will extend these results on the Herz spaces with constant exponents <span>(dot{K }_q^{alpha,p}({mathbb{R}}^n))</span> to one’s on the Herz spaces with variable exponent <span>(dot{K}_{q(cdot)}^{alpha,p}({mathbb{R}}^n))</span>. </p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"176 1","pages":"86 - 110"},"PeriodicalIF":0.6,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145165612","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":"Nontriviality of the module of relations for degree 4 polynomials","authors":"Á Serrano Holgado","doi":"10.1007/s10474-025-01541-3","DOIUrl":"10.1007/s10474-025-01541-3","url":null,"abstract":"<div><p>We characterize the nontriviality of the module of relations of an irreducible quartic polynomial in terms of a quotient between its roots. In the case where the base field is <span>(mathbb{Q})</span>, we also give a characterization in terms of the roots of the cubic resolvent of the polynomial.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"176 1","pages":"236 - 243"},"PeriodicalIF":0.6,"publicationDate":"2025-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145160931","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":"Operator relations characterizing higher-order differential operators","authors":"W. Fechner,&nbsp;E. Gselmann,&nbsp;A. Świątczak-Kolenda","doi":"10.1007/s10474-025-01540-4","DOIUrl":"10.1007/s10474-025-01540-4","url":null,"abstract":"<div><p>Let <span>(r)</span> be a positive integer, <span>(N)</span> a nonnegative integer and <span>(Omega subset mathbb{R}^{r})</span> be a domain. Further, for all multi-indices <span>(alpha in mathbb{N}^{r})</span>, <span>(|alpha|leq N)</span>, let us consider the partial differential operator <span>(D^{alpha})</span> defined by \u0000<span>(D^{alpha}= frac{partial^{|alpha|}}{partial x_{1}^{alpha_{1}}cdots partial x_{r}^{alpha_{r}}},)</span>where <span>(alpha= (alpha_{1}, ldots, alpha_{r}))</span>. Here, by definition, we mean <span>(D^{0}equiv mathrm{id})</span>. \u0000A straightforward computation shows that if <span>(f, gin mathscr{C}^{N}(Omega))</span> and <span>(alpha in mathbb{N}^{r})</span> with <span>(|alpha|leq N)</span>, then we have \u0000</p><div><div><span>$$D^{alpha}(fcdot g) = sum_{betaleq alpha}binom{alpha}{beta}D^{beta}(f)cdot D^{alpha - beta}(g).$$</span></div><div>\u0000 (*)\u0000 </div></div><p>\u0000This paper is devoted to the study of the identity <span>((ast))</span> in the space <span>(mathscr{C}(Omega))</span>. More precisely, if <span>(r)</span> is a positive integer, <span>(N)</span> is a nonnegative integer and <span>(Omega subset mathbb{R}^{r})</span> is a domain, then we describe all mappings (not necessarily linear) that satisfy the identity <span>((ast))</span> for all possible multi-indices <span>(alphain mathbb{N}^{r})</span>, <span>(|alpha|leq N)</span>. Our main result states that if the domain is <span>(mathscr{C}(Omega))</span>,\u0000then the mappings in question take a particularly specific form. Related results for the space <span>(mathscr{C}^{N}(Omega))</span> are also presented. </p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"176 1","pages":"264 - 275"},"PeriodicalIF":0.6,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-025-01540-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145169975","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}

{"title":"(d)-degree Erdős-Ko-Rado theorem for finite vector spaces","authors":"Y. Shan,&nbsp;J. Zhou","doi":"10.1007/s10474-025-01543-1","DOIUrl":"10.1007/s10474-025-01543-1","url":null,"abstract":"<div><p>Let <span>(V)</span> be an <span>(n)</span>-dimensional vector space over the finite field <span>(mathbb{F}_{q})</span> and let <span>(left[Vatop kright]_q)</span> denote the family of all <span>(k)</span>-dimensional subspaces of <span>(V)</span>. A family <span>(mathcal{F}subseteq left[Vatop kright]_q)</span> is called intersecting if for all <span>(F)</span>, <span>(F'inmathcal{F})</span>, we have <span>( dim (Fcap F')geq 1)</span>. Let <span>(delta_{d}(mathcal{F}))</span> denote the minimum degree in <span>(mathcal{F})</span> of all <span>(d)</span>-dimensional subspaces. In this paper we show that <span>(delta_{d}(mathcal{F})leq left[ n -d -1atop k -d -1right])</span> in any intersecting family <span>(mathcal{F}subseteq left[Vatop kright]_q)</span>, where <span>(k&gt;dgeq 2)</span> and <span>(ngeq 2k+1)</span>.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"176 1","pages":"215 - 235"},"PeriodicalIF":0.6,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145166832","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":"From Heegaard diagrams to surgery","authors":"J. Nikolić,&nbsp; V. Ovaskainen,&nbsp; Z. Petrić","doi":"10.1007/s10474-025-01532-4","DOIUrl":"10.1007/s10474-025-01532-4","url":null,"abstract":"<div><p>The precise steps of a procedure of going from Heegaard diagrams to framed link diagrams are introduced in this note.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"176 1","pages":"171 - 182"},"PeriodicalIF":0.6,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145166873","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":"Perimetric contraction principle on quadrilaterals in semimetric spaces with triangle functions","authors":"R. K. Bisht","doi":"10.1007/s10474-025-01539-x","DOIUrl":"10.1007/s10474-025-01539-x","url":null,"abstract":"<div><p>This paper investigates the perimetric contraction principle for quadrilaterals, a four-point extension of the Banach contraction principle, within the framework of semimetric spaces using triangle functions introduced by M. Bessenyei and Zs. Páles. We provide new insights into the fixed point theorem for perimetric contractions on quadrilaterals, demonstrating its applicability beyond metric spaces to include ultrametric spaces and distance spaces with power triangle functions. </p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"176 1","pages":"276 - 289"},"PeriodicalIF":0.6,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145166833","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":"Sums of Fourier coefficients of certain Eisenstein series of GL(5)","authors":"Ch. Shao,&nbsp;H. Zhang","doi":"10.1007/s10474-025-01544-0","DOIUrl":"10.1007/s10474-025-01544-0","url":null,"abstract":"<div><p>Let <span>(f)</span> be a Hecke-Maass cusp form for <span>(mathrm{SL}_2(mathbb{Z}))</span> with normalized Fourier coefficients <span>(lambda_f(n))</span> and Laplace eigenvalue <span>(1/4+mu_f^2)</span>. Let <span>(g)</span> be a Hecke-Maass cusp form for <span>(mathrm{SL}_2(mathbb{Z}))</span> with normalized Fourier coefficients <span>(lambda_g(n))</span>. In this paper, we study the asymptotic of <span>(sum_{n leq X}lambda_{1boxplus(ftimes g)}(n))</span> and get the explicit dependence of the error term on the spectral parameter <span>(mu_f)</span>.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"176 1","pages":"139 - 170"},"PeriodicalIF":0.6,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145166831","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}