Bulletin of the Australian Mathematical Society最新文献_第4页

EDGE WEIGHTING FUNCTIONS ON THE SEMITOTAL DOMINATING SET OF CLAW-FREE GRAPHS 无爪图半总支配集上的边加权函数

IF 0.7 4区数学

Bulletin of the Australian Mathematical Society Pub Date : 2024-02-12 DOI: 10.1017/s0004972724000017

JIE CHEN, HONGZHANG CHEN, SHOU-JUN XU

{"title":"EDGE WEIGHTING FUNCTIONS ON THE SEMITOTAL DOMINATING SET OF CLAW-FREE GRAPHS","authors":"JIE CHEN, HONGZHANG CHEN, SHOU-JUN XU","doi":"10.1017/s0004972724000017","DOIUrl":"https://doi.org/10.1017/s0004972724000017","url":null,"abstract":"In an isolate-free graph G, a subset S of vertices is a semitotal dominating set of G if it is a dominating set of G and every vertex in S is within distance 2 of another vertex of S. The semitotal domination number of G, denoted by $gamma _{t2}(G)$ , is the minimum cardinality of a semitotal dominating set in G. Using edge weighting functions on semitotal dominating sets, we prove that if $Gneq N_2$ is a connected claw-free graph of order $ngeq 6$ with minimum degree $delta (G)geq 3$ , then $gamma _{t2}(G)leq frac{4}{11}n$ and this bound is sharp, disproving the conjecture proposed by Zhu et al. [‘Semitotal domination in claw-free cubic graphs’, Graphs Combin.33(5) (2017), 1119–1130].","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"14 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139767182","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}

引用次数: 0

ON THE LIMIT SET OF A COMPLEX HYPERBOLIC TRIANGLE GROUP 上的复双曲三角形群的极限集

IF 0.7 4区数学

Bulletin of the Australian Mathematical Society Pub Date : 2024-02-02 DOI: 10.1017/s0004972723001478

MENGQI SHI, JIEYAN WANG

引用次数: 0

GENERALISED MUTUALLY PERMUTABLE PRODUCTS AND SATURATED FORMATIONS, II 广义互变积和饱和形成，ii

IF 0.7 4区数学

Bulletin of the Australian Mathematical Society Pub Date : 2024-01-30 DOI: 10.1017/s0004972723001430

ADOLFO BALLESTER-BOLINCHES, SESUAI Y. MADANHA, TENDAI M. MUDZIIRI SHUMBA, MARÍA C. PEDRAZA-AGUILERA

引用次数: 0

MULTIPLE SOLUTIONS FOR -LAPLACIAN EQUATIONS WITH NONLINEARITY SUBLINEAR AT ZERO 非线性为零的-拉普拉斯方程的多重解

IF 0.7 4区数学

Bulletin of the Australian Mathematical Society Pub Date : 2024-01-29 DOI: 10.1017/s0004972723001405

SHIBO LIU

{"title":"MULTIPLE SOLUTIONS FOR -LAPLACIAN EQUATIONS WITH NONLINEARITY SUBLINEAR AT ZERO","authors":"SHIBO LIU","doi":"10.1017/s0004972723001405","DOIUrl":"https://doi.org/10.1017/s0004972723001405","url":null,"abstract":"We consider the Dirichlet problem for $p(x)$ -Laplacian equations of the form $$ begin{align*} -Delta_{p(x)}u+b(x)vert uvert ^{p(x)-2}u=f(x,u),quad uin W_{0}^{1,p(x)}(Omega). end{align*} $$ The odd nonlinearity $f(x,u)$ is $p(x)$ -sublinear at $u=0$ but the related limit need not be uniform for $xin Omega $ . Except being subcritical, no additional assumption is imposed on $f(x,u)$ for $|u|$ large. By applying Clark’s theorem and a truncation method, we obtain a sequence of solutions with negative energy and approaching the zero function $u=0$ .","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"44 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139586220","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}

引用次数: 0

CONGRUENCES FOR RANKS OF PARTITIONS 分区等级的同余

IF 0.7 4区数学

Bulletin of the Australian Mathematical Society Pub Date : 2024-01-29 DOI: 10.1017/s0004972723001454

RENRONG MAO

引用次数: 0

HOMOLOGICAL LINEAR QUOTIENTS AND EDGE IDEALS OF GRAPHS 图的同源线性商和边沿理想

IF 0.7 4区数学

Bulletin of the Australian Mathematical Society Pub Date : 2024-01-29 DOI: 10.1017/s0004972723001363

NADIA TAGHIPOUR, SHAMILA BAYATI, FARHAD RAHMATI

{"title":"HOMOLOGICAL LINEAR QUOTIENTS AND EDGE IDEALS OF GRAPHS","authors":"NADIA TAGHIPOUR, SHAMILA BAYATI, FARHAD RAHMATI","doi":"10.1017/s0004972723001363","DOIUrl":"https://doi.org/10.1017/s0004972723001363","url":null,"abstract":"It is well known that the edge ideal <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001363_inline1.png\" /> <jats:tex-math> $I(G)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> of a simple graph <jats:italic>G</jats:italic> has linear quotients if and only if <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001363_inline2.png\" /> <jats:tex-math> $G^c$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> is chordal. We investigate when the property of having linear quotients is inherited by homological shift ideals of an edge ideal. We will see that adding a cluster to the graph <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001363_inline3.png\" /> <jats:tex-math> $G^c$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> when <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001363_inline4.png\" /> <jats:tex-math> $I(G)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> has homological linear quotients results in a graph with the same property. In particular, <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001363_inline5.png\" /> <jats:tex-math> $I(G)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> has homological linear quotients when <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001363_inline6.png\" /> <jats:tex-math> $G^c$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> is a block graph. We also show that adding pinnacles to trees preserves the property of having homological linear quotients for the edge ideal of their complements. Furthermore, <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001363_inline7.png\" /> <jats:tex-math> $I(G)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> has homological linear quotients for every graph <jats:italic>G</jats:italic> such that <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001363_inline8.png\" /> <jats:tex-math> $G^c$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> is a <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001363_inline9.png\" /> <jats:tex-math> $lambda $ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-min","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"38 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139586223","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}

引用次数: 0

ON THE CHARACTERISATION OF ALTERNATING GROUPS BY CODEGREES 关于交替群的编码度特征

IF 0.7 4区数学

Bulletin of the Australian Mathematical Society Pub Date : 2024-01-26 DOI: 10.1017/s0004972723001429

MALLORY DOLORFINO, LUKE MARTIN, ZACHARY SLONIM, YUXUAN SUN, YONG YANG

{"title":"ON THE CHARACTERISATION OF ALTERNATING GROUPS BY CODEGREES","authors":"MALLORY DOLORFINO, LUKE MARTIN, ZACHARY SLONIM, YUXUAN SUN, YONG YANG","doi":"10.1017/s0004972723001429","DOIUrl":"https://doi.org/10.1017/s0004972723001429","url":null,"abstract":"Let G be a finite group and $mathrm {Irr}(G)$ the set of all irreducible complex characters of G. Define the codegree of $chi in mathrm {Irr}(G)$ as $mathrm {cod}(chi ):={|G:mathrm {ker}(chi ) |}/{chi (1)}$ and let $mathrm {cod}(G):={mathrm {cod}(chi ) mid chi in mathrm {Irr}(G)}$ be the codegree set of G. Let $mathrm {A}_n$ be an alternating group of degree $n ge 5$ . We show that $mathrm {A}_n$ is determined up to isomorphism by $operatorname {cod}(mathrm {A}_n)$ .","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"31 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139586153","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}

引用次数: 0

COMPLETE EMBEDDINGS OF GROUPS 群的完全嵌入

IF 0.7 4区数学

Bulletin of the Australian Mathematical Society Pub Date : 2024-01-26 DOI: 10.1017/s0004972723001442

MARTIN R. BRIDSON, HAMISH SHORT

{"title":"COMPLETE EMBEDDINGS OF GROUPS","authors":"MARTIN R. BRIDSON, HAMISH SHORT","doi":"10.1017/s0004972723001442","DOIUrl":"https://doi.org/10.1017/s0004972723001442","url":null,"abstract":"Every countable group G can be embedded in a finitely generated group $G^*$ that is hopfian and complete, that is, $G^*$ has trivial centre and every epimorphism $G^*to G^*$ is an inner automorphism. Every finite subgroup of $G^*$ is conjugate to a finite subgroup of G. If G has a finite presentation (respectively, a finite classifying space), then so does $G^*$ . Our construction of $G^*$ relies on the existence of closed hyperbolic 3-manifolds that are asymmetric and non-Haken.","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"396 2 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139586224","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}

引用次数: 0

SOLVABLE GROUPS WHOSE NONNORMAL SUBGROUPS HAVE FEW ORDERS 非正常子群阶数少的可解群

IF 0.7 4区数学

Bulletin of the Australian Mathematical Society Pub Date : 2023-12-27 DOI: 10.1017/s0004972723001168

LIJUAN HE, HENG LV, GUIYUN CHEN

{"title":"SOLVABLE GROUPS WHOSE NONNORMAL SUBGROUPS HAVE FEW ORDERS","authors":"LIJUAN HE, HENG LV, GUIYUN CHEN","doi":"10.1017/s0004972723001168","DOIUrl":"https://doi.org/10.1017/s0004972723001168","url":null,"abstract":"Suppose that G is a finite solvable group. Let $t=n_c(G)$ denote the number of orders of nonnormal subgroups of G. We bound the derived length $dl(G)$ in terms of $n_c(G)$ . If G is a finite p-group, we show that $|G'|leq p^{2t+1}$ and $dl(G)leq lceil log _2(2t+3)rceil $ . If G is a finite solvable nonnilpotent group, we prove that the sum of the powers of the prime divisors of $|G'|$ is less than t and that $dl(G)leq lfloor 2(t+1)/3rfloor +1$ .","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"109 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139052909","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}

引用次数: 0

DIVISIBILITY OF SUMS OF PARTITION NUMBERS BY MULTIPLES OF 2 AND 3 2 和 3 的倍数分割数之和的可分割性

IF 0.7 4区数学

Bulletin of the Australian Mathematical Society Pub Date : 2023-12-22 DOI: 10.1017/s0004972723001351

Nayandeep Deka Baruah

{"title":"DIVISIBILITY OF SUMS OF PARTITION NUMBERS BY MULTIPLES OF 2 AND 3","authors":"Nayandeep Deka Baruah","doi":"10.1017/s0004972723001351","DOIUrl":"https://doi.org/10.1017/s0004972723001351","url":null,"abstract":"\u0000\t We show that certain sums of partition numbers are divisible by multiples of 2 and 3. For example, if \u0000\t \u0000\t\t\u0000\t\t\u0000$p(n)$\u0000\u0000\t \u0000\t denotes the number of unrestricted partitions of a positive integer n (and \u0000\t \u0000\t\t\u0000\t\t\u0000$p(0)=1$\u0000\u0000\t \u0000\t , \u0000\t \u0000\t\t\u0000\t\t\u0000$p(n)=0$\u0000\u0000\t \u0000\t for \u0000\t \u0000\t\t\u0000\t\t\u0000$n<0$\u0000\u0000\t \u0000\t ), then for all nonnegative integers m, \u0000\t \u0000\t\t\u0000\t\t\u0000$$ begin{align*}sum_{k=0}^infty p(24m+23-omega(-2k))+sum_{k=1}^infty p(24m+23-omega(2k))equiv 0~ (text{mod}~144),end{align*} $$\u0000\u0000\t \u0000\t \u0000\t where \u0000\t \u0000\t\t\u0000\t\t\u0000$omega (k)=k(3k+1)/2$\u0000\u0000\t \u0000\t .","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"3 9","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138945112","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}

引用次数: 0