Semigroup Forum最新文献_第5页

Finite semigroups and periodic sums systems in $$beta mathbb {N}$$ and their Ramsey theoretic consequences $$beta mathbb {N}$ 中的有限半群和周期和系统及其拉姆齐理论后果

IF 0.7 3区数学

Semigroup Forum Pub Date : 2024-04-05 DOI: 10.1007/s00233-024-10424-y

Yevhen Zelenyuk

{"title":"Finite semigroups and periodic sums systems in $$beta mathbb {N}$$ and their Ramsey theoretic consequences","authors":"Yevhen Zelenyuk","doi":"10.1007/s00233-024-10424-y","DOIUrl":"https://doi.org/10.1007/s00233-024-10424-y","url":null,"abstract":"Let (m,nge 2) and define (nu :omega rightarrow {0,ldots ,m-1}) by (nu (k)equiv kpmod {m}). We construct some new finite semigroups in (beta mathbb {N}), in particular, a semigroup generated by m elements of order n with cardinality (m^n+m^{n-1}+cdots +m). We also show that, for (nge m), there is a sequence (p_0,ldots ,p_{m-1}) in (beta mathbb {N}) such that all sums (sum _{j=i}^{i+k}p_{nu (j)}), where (iin {0,ldots ,m-1}) and (kin {0,ldots ,n-1}), are distinct and (sum _{j=i}^{i+n}p_{nu (j)}=sum _{j=i}^{i+n-m}p_{nu (j)}) for each i. As consequences we derive some new Ramsey theoretic results. In particular, we show that, for (nge m), there is a partition ({A_{i,k}:(i,k)in {0,ldots ,m-1}times {0,ldots ,n-1}}) of (mathbb {N}) such that, whenever for each (i, k), (mathscr {B}_{i,k}) is a finite partition of (A_{i,k}), there exist (B_{i,k}in mathscr {B}_{i,k}) and a sequence ((x_j)_{j=0}^infty ) such that for every finite sequence (j_0<ldots <j_s) such that (j_{t+1}equiv j_t+1pmod {m}) for each (t<s), one has (x_{j_0}+cdots +x_{j_s}in B_{i_0,k_0}), where (i_0=nu (j_0)) and (k_0) is s if (sle n-1) and (n-m+nu (s-n)) otherwise.","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":"75 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140577923","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

Set-theoretical solutions of the pentagon equation on Clifford semigroups 克利福德半群上五边形方程的集合论解

IF 0.7 3区数学

Semigroup Forum Pub Date : 2024-03-27 DOI: 10.1007/s00233-024-10421-1

Marzia Mazzotta, Vicent Pérez-Calabuig, Paola Stefanelli

引用次数: 0

The natural partial order on semigroups of transformations with restricted range that preserve an equivalence 保留等价性的限定范围变换半群上的自然偏序

IF 0.7 3区数学

Semigroup Forum Pub Date : 2024-03-27 DOI: 10.1007/s00233-024-10422-0

Kritsada Sangkhanan, Jintana Sanwong

引用次数: 0

Exponential stability of extensible beams equation with Balakrishnan–Taylor, strong and localized nonlinear damping 具有 Balakrishnan-Taylor、强和局部非线性阻尼的可扩展梁方程的指数稳定性

IF 0.7 3区数学

Semigroup Forum Pub Date : 2024-03-22 DOI: 10.1007/s00233-024-10419-9

Zayd Hajjej

引用次数: 0

Row-factorization matrices in Arf numerical semigroups and defining ideals Arf 数字半群中的行因子矩阵和定义理想

IF 0.7 3区数学

Semigroup Forum Pub Date : 2024-03-22 DOI: 10.1007/s00233-024-10416-y

Meral Süer, Mehmet Yeşil

引用次数: 0

The additively idempotent semiring $$S_7^0$$ is nonfinitely based 可加可幂等分线$$S_7^0$$是非无限基于的

IF 0.7 3区数学

Semigroup Forum Pub Date : 2024-03-20 DOI: 10.1007/s00233-024-10420-2

Yanan Wu, Miaomiao Ren, Xianzhong Zhao

引用次数: 0

On splittings and integration of almost periodic functions with and without geometry 关于有几何和无几何的几乎周期函数的分裂和积分

IF 0.7 3区数学

Semigroup Forum Pub Date : 2024-03-19 DOI: 10.1007/s00233-024-10415-z

Christian Budde, Josef Kreulich

引用次数: 0

Difference of Hilbert series of homogeneous monoid algebras and their normalizations 同质单元代数的希尔伯特级数差及其归一化

IF 0.7 3区数学

Semigroup Forum Pub Date : 2024-03-11 DOI: 10.1007/s00233-024-10414-0

引用次数: 0

Well-posedness of non-autonomous transport equation on metric graphs 度量图上非自治输运方程的好求性

IF 0.7 3区数学

Semigroup Forum Pub Date : 2024-03-06 DOI: 10.1007/s00233-024-10417-x

Christian Budde, Marjeta Kramar Fijavž

引用次数: 0

Combinatorial results for semigroups of orientation-preserving and order-decreasing transformations 保向和阶减变换半群的组合结果

IF 0.7 3区数学

Semigroup Forum Pub Date : 2024-02-23 DOI: 10.1007/s00233-024-10413-1

{"title":"Combinatorial results for semigroups of orientation-preserving and order-decreasing transformations","authors":"","doi":"10.1007/s00233-024-10413-1","DOIUrl":"https://doi.org/10.1007/s00233-024-10413-1","url":null,"abstract":"<h3>Abstract</h3> Let ({{mathscr {O}}{mathscr {P}}{mathscr {D}}}_{n}) be the semigroup consisting of all orientation-preserving and order-decreasing full transformations on the finite chain (X_{n}={1<cdots <n}) , and let (N({{mathscr {O}}{mathscr {P}}{mathscr {D}}}_{n})) be the subsemigroup consisting of all nilpotent elements of ({{mathscr {O}}{mathscr {P}}{mathscr {D}}}_{n}) . Moreover, for (1le rle n-1) , let $$begin{aligned} {{mathscr {O}}{mathscr {P}}{mathscr {D}}}(n,r) ={alpha in {{mathscr {O}}{mathscr {P}}{mathscr {D}}}_{n},:, |textrm{im},(alpha )|le r}, end{aligned}$$ and let (N({{mathscr {O}}{mathscr {P}}{mathscr {D}}}(n,r))) be the subsemigroup consisting of all nilpotent elements of ({{mathscr {O}}{mathscr {P}}{mathscr {D}}}(n,r)) . In this paper, we compute the cardinalities of ({{mathscr {O}}{mathscr {P}}{mathscr {D}}}_{n}) , (N({{mathscr {O}}{mathscr {P}}{mathscr {D}}}_{n})) , ({{mathscr {O}}{mathscr {P}}{mathscr {D}}}(n,r)) and (N({{mathscr {O}}{mathscr {P}}{mathscr {D}}}(n,r))) , and find their ranks. Moreover, for each idempotent (xi ) in ({{mathscr {O}}{mathscr {P}}{mathscr {D}}}_{n}) , we show that ({{mathscr {O}}{mathscr {P}}{mathscr {D}}}_{n}(xi )={ alpha in {{mathscr {O}}{mathscr {P}}{mathscr {D}}}_{n} , alpha ^{m}=xi ,, text{ for } text{ some } ,, min {mathbb {N}} }) is the maximal nilpotent subsemigroup of ({{mathscr {O}}{mathscr {P}}{mathscr {D}}}_{n}) with zero (xi ) , and we find its cardinality and rank.","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":"12 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139953366","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