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New recursive constructions of amoebas and their balancing number 阿米巴虫的新递归结构及其平衡数
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2025-04-10 DOI: 10.1007/s00010-025-01156-7
Laura Eslava, Adriana Hansberg, Tonatiuh Matos-Wiederhold, Denae Ventura
{"title":"New recursive constructions of amoebas and their balancing number","authors":"Laura Eslava,&nbsp;Adriana Hansberg,&nbsp;Tonatiuh Matos-Wiederhold,&nbsp;Denae Ventura","doi":"10.1007/s00010-025-01156-7","DOIUrl":"10.1007/s00010-025-01156-7","url":null,"abstract":"<div><p>Amoeba graphs are based on iterative <i>feasible edge-replacements</i>, where, at each step, an edge from the graph is removed and placed in an available spot so that the resulting graph is isomorphic to the original graph. Broadly speaking, amoebas are graphs that, by means of a chain of feasible edge-replacements, can be transformed into any other copy of itself on a given vertex set (depending on which they are defined as local or global amoebas). Global amoebas were born as examples of <i>balanceable</i> graphs, which appear with half of their edges in each color in any 2-edge coloring of a large enough complete graph with a sufficient amount of edges <i>k</i> in each color. The minimum value of <i>k</i> is called the <i>balancing number</i> of <i>G</i>. We provide a recursive construction to generate very diverse infinite families of local and global amoebas, which not only answers a question posed by Caro et al. but also yields an efficient algorithm that provides a chain of feasible edge-replacements that one can perform in order to move a local amoeba into an aimed copy in the same vertex set. All results are illustrated by three different families of local amoebas, including the Fibonacci-type trees. We express the balancing number of a global amoeba <i>G</i> in terms of the extremal number of a class of subgraphs of <i>G</i> and give a general lower bound. We provide linear lower and upper bounds for the balancing number of our three case studies.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 3","pages":"1265 - 1299"},"PeriodicalIF":0.9,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144073919","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}
引用次数: 0
Analytical aspects of a q, r-analogue of poly-Stirling numbers of both kinds 两类聚斯特林数的q， r模拟的解析方面
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2025-02-22 DOI: 10.1007/s00010-024-01135-4
Takao Komatsu, Eli Bagno, David Garber
{"title":"Analytical aspects of a q, r-analogue of poly-Stirling numbers of both kinds","authors":"Takao Komatsu,&nbsp;Eli Bagno,&nbsp;David Garber","doi":"10.1007/s00010-024-01135-4","DOIUrl":"10.1007/s00010-024-01135-4","url":null,"abstract":"<div><p>The Stirling numbers of type <i>B</i> of the second kind count signed set partitions. In this paper, we provide new combinatorial and analytical identities regarding these numbers as well as Broder’s <i>r</i>-version of these numbers. Among these identities one can find recursions, explicit formulas based on the inclusion–exclusion principle, and also exponential generating functions. These Stirling numbers can be considered as members of a wider family of triangles of numbers that are characterized using results of Comtet and Lancaster. We generalize these theorems, which present equivalent conditions for a triangle of numbers to be a triangle of generalized Stirling numbers, to the case of the <i>q</i>, <i>r</i>-poly Stirling numbers, which are <i>q</i>-analogues of the restricted Stirling numbers defined by Broder and having a polynomial value appearing in their defining recursion. There are two ways to do this and these ways are related by a nice identity.\u0000</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 2","pages":"287 - 320"},"PeriodicalIF":0.9,"publicationDate":"2025-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143871400","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}
引用次数: 0
Orthogonality induced by norm derivatives: a new geometric constant and symmetry 范数导数诱导的正交性：一种新的几何常数和对称性
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2025-01-28 DOI: 10.1007/s00010-025-01154-9
Souvik Ghosh, Kallol Paul, Debmalya Sain
{"title":"Orthogonality induced by norm derivatives: a new geometric constant and symmetry","authors":"Souvik Ghosh,&nbsp;Kallol Paul,&nbsp;Debmalya Sain","doi":"10.1007/s00010-025-01154-9","DOIUrl":"10.1007/s00010-025-01154-9","url":null,"abstract":"<div><p>In this article we study the difference between orthogonality induced by norm derivatives (known as <span>(rho )</span>-orthogonality) and Birkhoff-James orthogonality in a normed linear space <span>(mathbb {X})</span> by introducing a new geometric constant, denoted by <span>(Gamma (mathbb {X}).)</span> We explore the relation between various geometric properties of the space and the constant <span>(Gamma (mathbb {X}).)</span> We also investigate the left symmetric and right symmetric elements of a normed linear space with respect to <span>(rho )</span>-orthogonality and obtain a characterization of the same. We characterize inner product spaces among normed linear spaces using the symmetricity of <span>(rho )</span>-orthogonality. Finally, we provide a complete description of both left symmetric and right symmetric elements with respect to <span>(rho )</span>-orthogonality for some particular Banach spaces.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 3","pages":"883 - 904"},"PeriodicalIF":0.9,"publicationDate":"2025-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144073898","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}
引用次数: 0
On composition and Right Distributive Law for formal power series of multiple variables 多变量形式幂级数的复合与右分配律
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2025-01-23 DOI: 10.1007/s00010-024-01152-3
Dariusz Bugajewski, Alessia Galimberti, Piotr Maćkowiak
{"title":"On composition and Right Distributive Law for formal power series of multiple variables","authors":"Dariusz Bugajewski,&nbsp;Alessia Galimberti,&nbsp;Piotr Maćkowiak","doi":"10.1007/s00010-024-01152-3","DOIUrl":"10.1007/s00010-024-01152-3","url":null,"abstract":"<div><p>In the first part of the paper we prove a necessary and sufficient condition for the existence of the composition of formal power series in the case when the outer series is a series of one variable while the inner one is a series of multiple variables. The aim of the second part is to remove ambiguities connected with the Right Distributive Law for formal power series of one variable as well as to provide analogues of that law in the multivariable case.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 1","pages":"21 - 35"},"PeriodicalIF":0.9,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143554185","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}
引用次数: 0
Characterizations of weighted generalized inverses 加权广义逆的刻画
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2025-01-20 DOI: 10.1007/s00010-024-01151-4
Bibekananda Sitha, Ratikanta Behera, Jajati Keshari Sahoo, R. N. Mohapatra, Predrag Stanimirović, Alena Stupina
{"title":"Characterizations of weighted generalized inverses","authors":"Bibekananda Sitha,&nbsp;Ratikanta Behera,&nbsp;Jajati Keshari Sahoo,&nbsp;R. N. Mohapatra,&nbsp;Predrag Stanimirović,&nbsp;Alena Stupina","doi":"10.1007/s00010-024-01151-4","DOIUrl":"10.1007/s00010-024-01151-4","url":null,"abstract":"<div><p>The main objective of this study is to introduce unique representations and characterizations for the several classes of weighted generalized inverses of matrices. Proposed representations of the matrix-weighted core inverse will help us to discuss some results associated with the reverse order law for these inverses. Furthermore, this paper introduces an extension of the concepts of generalized bilateral inverse and their respective dual for complex rectangular matrices. Characteristics that lead to self-duality in weighted bilateral inverses are also examined. In addition, a W-weighted index-MP, W-weighted MP-index, and W-weighted MP-index-MP matrices for rectangular complex matrices are introduced.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 3","pages":"1301 - 1336"},"PeriodicalIF":0.9,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144074172","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}
引用次数: 0
Some moduli related to (rho _{pm })-orthogonalities and semi-orthogonality in Banach spaces Banach空间中与(rho _{pm }) -正交和半正交有关的几个模
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2025-01-20 DOI: 10.1007/s00010-025-01153-w
Dandan Du, Yongjin Li
{"title":"Some moduli related to (rho _{pm })-orthogonalities and semi-orthogonality in Banach spaces","authors":"Dandan Du,&nbsp;Yongjin Li","doi":"10.1007/s00010-025-01153-w","DOIUrl":"10.1007/s00010-025-01153-w","url":null,"abstract":"<div><p>In this article, we introduce several new moduli of convexity connected with <span>(rho _{pm })</span>-orthogonalities and semi-orthogonality, which are closely related to the modulus of convexity <span>(delta _{X}(varepsilon ))</span>. In particular, these new parameters are computed for <i>X</i> being some specific spaces. Moreover, we give some applications of these two coefficients <span>(delta _{perp }(rho _{pm }, X))</span> and investigate the relation between these two parameters and the approximate symmetry of <span>(rho _{-})</span>-orthogonality. In the meantime, we give characterization of the Radon plane with an affine-hexagonal unit sphere in terms of these new moduli of convexity. Moreover, we also consider the moduli of smoothness related to <span>(rho _{pm })</span>-orthgonalities and semi-orthogonality. In the end, we discuss some applications of these new moduli of smoothness and study some relationships between these new parameters and uniform non-squareness, uniform convexity.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 3","pages":"905 - 926"},"PeriodicalIF":0.9,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144074171","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}
引用次数: 0
Sorting 1-away permutations with underlying Fibonacci convolutions 用潜在的斐波那契卷积排序1-差排列
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2025-01-19 DOI: 10.1007/s00010-024-01146-1
Hosam Mahmoud
{"title":"Sorting 1-away permutations with underlying Fibonacci convolutions","authors":"Hosam Mahmoud","doi":"10.1007/s00010-024-01146-1","DOIUrl":"10.1007/s00010-024-01146-1","url":null,"abstract":"<div><p>We discuss some combinatorics associated with 1-away permutations, where an element can be displaced from its correct position by at most one location. Specifically, we look at a sorting algorithm for such permutations and analyze its number of comparisons, <span>(C_n)</span>. We find that the mean is a certain combination of two-fold convolutions of Fibonacci numbers and the variance is a certain combination of three-fold convolutions of Fibonacci numbers, with corresponding asymptotics (as <span>(nrightarrow infty )</span>): </p><div><div><span>$${mathbb {E}}[C_n] sim frac{5 + sqrt{5}}{10}, n, qquad {mathbb {V}textrm{ar}}[C_n]sim frac{sqrt{5}}{25} , n.$$</span></div></div><p>The proofs contain finer asymptotics down to exponentially small error terms. The relatively small variance admits a weak law and a central limit theorem via a super moment generating function. In view of the special nature of the data, such a specialized algorithm outperforms general comparison-based sorting algorithms.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 3","pages":"1209 - 1219"},"PeriodicalIF":0.9,"publicationDate":"2025-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01146-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144073662","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}
引用次数: 0
Correction to: On the solvability of the (SSIE) with operator ({D}_{x} {mathbf { * }}left( { s}_{ R}^{{textbf{0}}} right) _{{{{Sigma }} - {lambda I}}} {{ subset }}{ s}_{ R}^{{{0}}} ), involving the fine spectrum of an operator 修正：关于（SSIE）与算子({D}_{x} {mathbf { * }}left( { s}_{ R}^{{textbf{0}}} right) _{{{{Sigma }} - {lambda I}}} {{ subset }}{ s}_{ R}^{{{0}}} )的可解性，涉及算子的精细谱
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2025-01-15 DOI: 10.1007/s00010-024-01142-5
Bruno de Malafosse, Eberhard Malkowsky, Vladinir Rakočević
{"title":"Correction to: On the solvability of the (SSIE) with operator ({D}_{x} {mathbf { * }}left( { s}_{ R}^{{textbf{0}}} right) _{{{{Sigma }} - {lambda I}}} {{ subset }}{ s}_{ R}^{{{0}}} ), involving the fine spectrum of an operator","authors":"Bruno de Malafosse,&nbsp;Eberhard Malkowsky,&nbsp;Vladinir Rakočević","doi":"10.1007/s00010-024-01142-5","DOIUrl":"10.1007/s00010-024-01142-5","url":null,"abstract":"","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 2","pages":"823 - 824"},"PeriodicalIF":0.9,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143871356","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}
引用次数: 0
Congruence properties of Lehmer-Euler numbers Lehmer-Euler数的同余性质
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2025-01-10 DOI: 10.1007/s00010-024-01150-5
Takao Komatsu, Guo-Dong Liu
{"title":"Congruence properties of Lehmer-Euler numbers","authors":"Takao Komatsu,&nbsp;Guo-Dong Liu","doi":"10.1007/s00010-024-01150-5","DOIUrl":"10.1007/s00010-024-01150-5","url":null,"abstract":"<div><p>Certain generalization of Euler numbers was defined in 1935 by Lehmer using cubic roots of unity, as a natural generalization of Bernoulli and Euler numbers. In this paper, Lehmer’s generalized Euler numbers are studied to give certain congruence properties together with recurrence and explicit formulas of the numbers. We also show a new polynomial sequence and its properties. Some identities including Euler and central factorial numbers are obtained.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 3","pages":"1337 - 1355"},"PeriodicalIF":0.9,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144074048","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}
引用次数: 0
Note on the variance of generalized random polygons 注意广义随机多边形的方差
IF 0.9 3区 数学
Aequationes Mathematicae Pub Date : 2025-01-10 DOI: 10.1007/s00010-024-01147-0
Ferenc Fodor, Balázs Grünfelder
{"title":"Note on the variance of generalized random polygons","authors":"Ferenc Fodor,&nbsp;Balázs Grünfelder","doi":"10.1007/s00010-024-01147-0","DOIUrl":"10.1007/s00010-024-01147-0","url":null,"abstract":"<div><p>We consider a probability model in which the hull of a sample of i.i.d. uniform random points from a convex disc <i>K</i> is formed by the intersection of all translates of another suitable fixed convex disc <i>L</i> that contain the sample. Such an object is called a random <i>L</i>-polygon in <i>K</i>. We assume that both <i>K</i> and <i>L</i> have <span>(C^2_+)</span> smooth boundaries, and we prove upper bounds on the variance of the number of vertices and missed area of random <i>L</i>-polygons assuming different curvature conditions. We also transfer some of our result to a circumscribed variant of this model.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 3","pages":"869 - 882"},"PeriodicalIF":0.9,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00010-024-01147-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144073844","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}
引用次数: 0
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