Advances in Applied Mathematics最新文献

Recursive properties of the characteristic polynomial of weighted lattices 加权格特征多项式的递推性质

IF 1.3 3区数学

Advances in Applied Mathematics Pub Date : 2026-05-01 Epub Date: 2026-01-27 DOI: 10.1016/j.aam.2026.103046

Gianira N. Alfarano , Eimear Byrne

引用次数: 0

On the second-largest modulus among the eigenvalues of a power hypergraph 幂超图特征值中的第二模

IF 1.3 3区数学

Advances in Applied Mathematics Pub Date : 2026-05-01 Epub Date: 2026-02-03 DOI: 10.1016/j.aam.2026.103052

Changjiang Bu , Lixiang Chen , Yongtang Shi

{"title":"On the second-largest modulus among the eigenvalues of a power hypergraph","authors":"Changjiang Bu , Lixiang Chen , Yongtang Shi","doi":"10.1016/j.aam.2026.103052","DOIUrl":"10.1016/j.aam.2026.103052","url":null,"abstract":"<div><div>It is well known that the algebraic multiplicity of an eigenvalue of a graph (or real symmetric matrix) is equal to the dimension of its corresponding linear eigen-subspace, also known as the geometric multiplicity. However, for hypergraphs, the relationship between these two multiplicities remains an open problem. For a graph <math><mi>G</mi><mo>=</mo><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></math> and <math><mi>k</mi><mo>≥</mo><mn>3</mn></math>, the k-power hypergraph <math><msup><mrow><mi>G</mi></mrow><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup></math> is a k-uniform hypergraph obtained by adding <math><mi>k</mi><mo>−</mo><mn>2</mn></math> new vertices to each edge of G, who always has non-real eigenvalues. In this paper, we determine the second-largest modulus Λ among the eigenvalues of <math><msup><mrow><mi>G</mi></mrow><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup></math>, which is indeed an eigenvalue of <math><msup><mrow><mi>G</mi></mrow><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup></math>. The projective eigenvariety <math><msub><mrow><mi>V</mi></mrow><mrow><mi>Λ</mi></mrow></msub></math> associated with Λ is the set of the eigenvectors of <math><msup><mrow><mi>G</mi></mrow><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup></math> corresponding to Λ considered in the complex projective space. We show that the dimension of <math><msub><mrow><mi>V</mi></mrow><mrow><mi>Λ</mi></mrow></msub></math> is zero, i.e., there are finitely many eigenvectors corresponding to Λ up to a scalar. We give both the algebraic multiplicity of Λ and the total multiplicity of the eigenvector in <math><msub><mrow><mi>V</mi></mrow><mrow><mi>Λ</mi></mrow></msub></math> in terms of the number of the weakest edges of G. Our results show that these two multiplicities are equal.</div></div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":"176 ","pages":"Article 103052"},"PeriodicalIF":1.3,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146190640","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

R-hulloid of the vertices of a tetrahedron 四面体顶点的r -壳体

IF 1.3 3区数学

Advances in Applied Mathematics Pub Date : 2026-05-01 Epub Date: 2026-02-10 DOI: 10.1016/j.aam.2026.103056

Marco Longinetti , Simone Naldi , Adriana Venturi

{"title":"R-hulloid of the vertices of a tetrahedron","authors":"Marco Longinetti , Simone Naldi , Adriana Venturi","doi":"10.1016/j.aam.2026.103056","DOIUrl":"10.1016/j.aam.2026.103056","url":null,"abstract":"<div><div>The R-hulloid, in the Euclidean space <math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math>, of the set of vertices V of a tetrahedron T is the minimal closed set containing V such that its complement is the union of open balls of radius R. When R is greater than the circumradius of T, the boundary of the R-hulloid consists of V and possibly of four spherical subsets of well defined spheres of radius R through the vertices of T. The existence of a value <math><msup><mrow><mi>R</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math> such that these subsets collapse into a point <math><msup><mrow><mi>O</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math>, in the interior of T, is investigated; in such a case <math><msup><mrow><mi>O</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math> belongs to four spheres of radius <math><msup><mrow><mi>R</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math>, each one through three vertices of T and not containing the fourth one. As a consequence, the range of ρ such that V is a ρ-body is described completely. This work generalizes to dimension three previous results, proved in the planar case and related to the three circles Johnson's Theorem.</div></div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":"176 ","pages":"Article 103056"},"PeriodicalIF":1.3,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146190620","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

Asymptotic weighted approximation of convex functions 凸函数的渐近加权逼近

IF 1.3 3区数学

Advances in Applied Mathematics Pub Date : 2026-05-01 Epub Date: 2026-02-09 DOI: 10.1016/j.aam.2026.103057

Fernanda Moreira Baêta

引用次数: 0

Leading coefficient in the Hankel determinants related to binomial and q-binomial transforms 与二项式和q-二项式变换有关的汉克尔行列式的前导系数

IF 1.3 3区数学

Advances in Applied Mathematics Pub Date : 2026-05-01 Epub Date: 2026-01-27 DOI: 10.1016/j.aam.2026.103051

Shane Chern , Lin Jiu , Shuhan Li , Liuquan Wang

引用次数: 0

A categorification of the Brenti–Welker identity Brenti-Welker身份的分类

IF 1.3 3区数学

Advances in Applied Mathematics Pub Date : 2026-05-01 Epub Date: 2026-01-23 DOI: 10.1016/j.aam.2026.103048

Deke Zhao , Zhankui Xiao

引用次数: 0

The generalized q-heat equations for q-3D hypergeometric polynomials with applications to generating functions and Askey–Wilson integrals q-3D超几何多项式的广义q-热方程及其在生成函数和Askey-Wilson积分中的应用

IF 1.3 3区数学

Advances in Applied Mathematics Pub Date : 2026-05-01 Epub Date: 2026-01-28 DOI: 10.1016/j.aam.2026.103054

Jian Cao

引用次数: 0

A multidimensional Rado Theorem 多维拉多定理

IF 1.3 3区数学

Advances in Applied Mathematics Pub Date : 2026-05-01 Epub Date: 2026-01-28 DOI: 10.1016/j.aam.2026.103050

Aaron Robertson

引用次数: 0

Combinatorial Hopf algebras from restriction species with preorder cuts 具有序切限制种的组合Hopf代数

IF 1.3 3区数学

Advances in Applied Mathematics Pub Date : 2026-05-01 Epub Date: 2026-02-12 DOI: 10.1016/j.aam.2026.103055

Gunnar Fløystad

{"title":"Combinatorial Hopf algebras from restriction species with preorder cuts","authors":"Gunnar Fløystad","doi":"10.1016/j.aam.2026.103055","DOIUrl":"10.1016/j.aam.2026.103055","url":null,"abstract":"<div><div>We get new Hopf algebras (HA): 1. A wealth of quotient HA's of the Malvenuto-Reutenauer HA (the Loday-Ronco HA being a special case). They consist of the permutations avoiding an arbitrary set of permutations without global descents, 2. A HA of pairs of parking filtrations, and 3. Four HA of pairs of preorders.</div><div>New concepts in this setting are: 1. a category <math><mi>se</mi><msub><mrow><mi>t</mi></mrow><mrow><mi>N</mi></mrow></msub></math> whose objects are sets, but morphisms are represented by matrices of natural numbers, and 2. restriction species <math><mi>S</mi></math> on sets coming with pairs of natural transformations <math><msub><mrow><mi>π</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>:</mo><mi>S</mi><mo>→</mo><mrow><mi>Pre</mi></mrow></math> to the species of preorders. These induce two coproducts <math><msub><mrow><mi>Δ</mi></mrow><mrow><mn>1</mn></mrow></msub></math> and <math><msub><mrow><mi>Δ</mi></mrow><mrow><mn>2</mn></mrow></msub></math>. Dualizing <math><msub><mrow><mi>Δ</mi></mrow><mrow><mn>1</mn></mrow></msub></math> gives product <math><msub><mrow><mi>μ</mi></mrow><mrow><mn>1</mn></mrow></msub></math> and coproduct <math><msub><mrow><mi>Δ</mi></mrow><mrow><mn>2</mn></mrow></msub></math>, giving bimonoid species.</div></div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":"176 ","pages":"Article 103055"},"PeriodicalIF":1.3,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146190619","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

Pre-signed graphs: A reformulation of signed graphs and their embeddings 预符号图：符号图及其嵌入的重新表述

IF 1.3 3区数学

Advances in Applied Mathematics Pub Date : 2026-05-01 Epub Date: 2026-02-03 DOI: 10.1016/j.aam.2026.103053

Yichao Chen

引用次数: 0