{"title":"Steiner coset partitions for five mutually commuting subgroups","authors":"Fusun Akman, Papa Sissokho","doi":"10.1007/s10474-026-01635-6","DOIUrl":"10.1007/s10474-026-01635-6","url":null,"abstract":"<div><p>A <i>Steiner coset partition</i> of a group <i>G</i> with respect to pairwise distinct subgroups <span>(H_1)</span>, ..., <span>(H_r)</span> is a collection of pairwise disjoint cosets <span>(g_1H_1)</span>, ..., <span>(g_rH_r)</span> whose union is <i>G</i>. Motivated by the <i>Herzog–Schönheim Conjecture</i>, we have recently started exploring the groups that admit Steiner coset partitions. In previous work, we completely classified such groups for up to <span>(r=4)</span> mutually commuting subgroups. In this paper, we extend the classification to <span>(r=5)</span> mutually commuting subgroups.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"179 1","pages":"254 - 265"},"PeriodicalIF":0.6,"publicationDate":"2026-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-026-01635-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176563","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":"On some examples and counterexamples about weighted Lagrange interpolation with Exponential and Hermite weights","authors":"Patricia Szokol","doi":"10.1007/s10474-026-01634-7","DOIUrl":"10.1007/s10474-026-01634-7","url":null,"abstract":"<div><p>The famous Bernstein conjecture about optimal node systems in classical polynomial Lagrange interpolation, standing unresolved for about half a century, was solved by T. Kilgore in 1978. Immediately after him, the additional conjecture of Erdős was also solved by de Boor and Pinkus. These breakthrough achievements were built on a fundamental auxiliary result on the nonsingularity of derivative (Jacobian) matrices of certain interval maxima in the function of the nodes. After the above breakthrough, a considerable effort was made to extend the results to the case of at least certain Chebyshev–Haar spaces of functions. Here, we analyze to what extent the key nonsingularity statement remains true in the case of exponentially weighted interpolation on the half-line, or with Hermite weights on the full real line. In these settings, counterexamples demonstrate that the respective derivative matrices may as well be singular. It remains to further study whether the Bernstein- and Erdős characterizations remain valid. The “hybrid” Chebyshev–Haar system of exponentially weighted polynomials adjoined with constant functions and the corresponding interpolation were previously studied as well. Some hints were also given for the proof of the respective Bernstein and Erdös conjectures. We present in detail the full proof together with all the auxiliary results needed in this setting.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"179 1","pages":"219 - 253"},"PeriodicalIF":0.6,"publicationDate":"2026-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-026-01634-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176620","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":"Fourier-analytic derivation of Hardy-type oscillatory identity for p-circle domains by generalized Bessel functions","authors":"Masaya Kitajima","doi":"10.1007/s10474-026-01632-9","DOIUrl":"10.1007/s10474-026-01632-9","url":null,"abstract":"<div><p>Using Fourier-analytic methods, we derive a Hardy-type oscillatory identity for the family of planar domains <span>({xin mathbb {R}^{2} mid |x_1|^p + |x_2|^p le r^p})</span> with positive <i>p</i> satisfying <span>((2/p) in mathbb {N})</span>. This identity generalizes the classical <i>Hardy’s identity</i> for the Euclidean disk, arising from the Poisson summation formula. For these domains of non-smooth curves (including the <i>astroid</i>), the rotational symmetry of the Fourier transform is lost, so it cannot be expressed using classical Bessel functions. To address this, we introduce a family of generalized Bessel functions naturally arising from the Fourier transform of <i>p</i>-radial functions. These functions capture the oscillatory structure induced by the loss of rotational symmetry and provide the analytic framework for Hardy-type identities between these domains. While classical motivations relate to estimating lattice point errors in number theory, we focus here on deriving the identities themselves and understanding their structure.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"179 1","pages":"204 - 218"},"PeriodicalIF":0.6,"publicationDate":"2026-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-026-01632-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176369","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":"The minimal common difference of Erdős’ infinite arithmetic progressions","authors":"Yong-Gao Chen","doi":"10.1007/s10474-026-01637-4","DOIUrl":"10.1007/s10474-026-01637-4","url":null,"abstract":"<div><p>Let <span>(mathcal {E})</span> be the set of positive odd numbers that cannot be represented as the sum of a prime and a power of two. In 1950, Erdős proved that <span>(mathcal {E})</span> contains an infinite arithmetic progression. In this paper, it is proved that if <span>({ mh+a: h=0,1,dots } subseteq mathcal {E})</span>, then <span>(mge 11184810)</span> and <i>m</i> has at least seven distinct prime divisors. Furthermore, these lower bounds are best possible.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"179 1","pages":"196 - 203"},"PeriodicalIF":0.6,"publicationDate":"2026-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176756","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":"Orthoisomorphisms of idempotents of certain unital (C^*)-algebras","authors":"Fouzia Shaheen, Ahmed Al-Rawashdeh","doi":"10.1007/s10474-026-01631-w","DOIUrl":"10.1007/s10474-026-01631-w","url":null,"abstract":"<div><p>Al-Rawashdeh studied the induced map between the projections and he proved that it is an orthoisomorphism for a large class of <span>(C^*)</span>-algebras. In this paper, we extend the results of Al-Rawashdeh by replacing <span>(mathcal {U}(mathcal {A}))</span> with <span>(GL(mathcal {A}),)</span> and <span>(mathcal {P}(mathcal {A}))</span> with <span>(mathcal {I}(mathcal {A}))</span>. We prove that the induced map of idempotents is an orthoisomorphism for large class of simple, unital <span>(C^*)</span>-algebras of real rank zero with cancellation and having 2-divisible <span>(K_{0})</span>-groups, Cuntz algebras, and for simple, unital purely infinite <span>(C^*)</span>-algebras having 2-divisible <span>(K_{0})</span>-groups.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"179 1","pages":"184 - 195"},"PeriodicalIF":0.6,"publicationDate":"2026-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176419","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 bound on the equivariant unknotting number","authors":"Sarah Zampa","doi":"10.1007/s10474-026-01625-8","DOIUrl":"10.1007/s10474-026-01625-8","url":null,"abstract":"<div><p>We study how the equivariant signature of strongly invertible knots changes when one of the Boyle–Chen equivariant crossing change moves is applied. It follows from our results that the absolute value of the equivariant signature introduced by Alfieri–Boyle gives a lower bound to three times the equivariant unknotting number.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"179 1","pages":"163 - 183"},"PeriodicalIF":0.6,"publicationDate":"2026-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-026-01625-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176421","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":"Classification of quaternionic projective transformations by equicontinuity regions","authors":"Sandipan Dutta, Krishnendu Gongopadhyay, Rahul Mondal","doi":"10.1007/s10474-026-01628-5","DOIUrl":"10.1007/s10474-026-01628-5","url":null,"abstract":"<div><p>We describe the equicontinuity regions of cyclic subgroups of the quaternionic projective linear group <span>(textrm{PSL}(n+1,mathbb {H}))</span>. We show that these regions depend solely on the dynamical type of the generator <i>g</i>, i.e., whether <i>g</i> is elliptic, parabolic, loxodromic or loxoparabolic. This yields an analytic interpretation of the dynamical classification of the elements. In particular, elliptic cyclic groups act equicontinuously on all of the quaternionic projective space, while for the parabolic, loxodromic and loxoparabolic elements the equicontinuity region is determined by explicit quaternionic projective subspaces arising from the generator’s Jordan form.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"179 1","pages":"149 - 162"},"PeriodicalIF":0.6,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176794","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":"Frequent, disjoint hypercyclicity and strong topological transitivity of generalized weighted shift operators on Hilbert (C^{*})-modules","authors":"Song-Ung Ri, Hyon-Hui Ju, Jin-Myong Kim","doi":"10.1007/s10474-026-01627-6","DOIUrl":"10.1007/s10474-026-01627-6","url":null,"abstract":"<div><p>In this paper, we study some dynamical properties such as the Frequent Hypercyclicity Criterion, chaos, disjoint hypercyclicity and <span>(mathcal {F})</span>-transitivity via the Furstenberg family <span>(mathcal {F})</span> for generalized bilateral weighted shift operators on the standard Hilbert <span>(C^{*})</span>-module over the <span>(C^{*})</span>-algebra of compact operators on a separable Hilbert space.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"179 1","pages":"131 - 148"},"PeriodicalIF":0.6,"publicationDate":"2026-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176867","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":"Rational link fertility","authors":"Andrew Ducharme","doi":"10.1007/s10474-026-01619-6","DOIUrl":"10.1007/s10474-026-01619-6","url":null,"abstract":"<div><p>A knot <i>K</i> is the resultant of a knot <i>H</i> if there exists a minimal crossing diagram <i>D</i> of <i>H</i> such that some crossings of <i>D</i> can be altered to produce <i>K</i>. <i>H</i> is fertile if every prime knot <i>K</i> with crossing number less than <i>c</i>(<i>H</i>) is a resultant of <i>H</i>. <i>H</i> has fertility number <i>n</i> if every prime knot <i>K</i> with crossing number less than or equal to <i>n</i> is a resultant of <i>H</i>. We classify the fertility and fertility number of all rational links. This requires the introduction of the analogous concept of link fertility. We find <span>(2^2_1)</span>, <span>(4^2_1)</span>, <span>(5^2_1)</span>, <span>(6^2_2)</span>, <span>(6^2_3)</span>, and <span>(7^2_2)</span> are fertile and <span>(6^2_1)</span> is not. We establish that almost all two-component links have fertility number greater than or equal to five.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"179 1","pages":"106 - 130"},"PeriodicalIF":0.6,"publicationDate":"2026-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-026-01619-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176784","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":"Exploring critical cardinalities via selection principles and games","authors":"Nur Alam, Debraj Chandra","doi":"10.1007/s10474-026-01623-w","DOIUrl":"10.1007/s10474-026-01623-w","url":null,"abstract":"<div><p>The study of cardinal characteristics <span>(mathfrak {b})</span> and <span>(mathfrak {d})</span> is well known in set-theoretic and general topology. In this paper, we present characterizations of <span>(mathfrak {b})</span> and <span>(mathfrak {d})</span> using selective properties, sub-bounded and sub-dominating families. In addition, we define infinitely long two-player games to present other characterizations of the critical cardinalities <span>(mathfrak {b})</span> and <span>(mathfrak {d})</span>.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"179 1","pages":"87 - 105"},"PeriodicalIF":0.6,"publicationDate":"2026-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149176507","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}