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On the $$A_{alpha }$$-Spectra of Some Join Graphs 关于一些连接图的$$A_{alpha }$$ -谱
Pub Date : 2020-08-24 DOI: 10.1007/s40840-021-01166-z
M. Basunia, Iswar Mahato, M. Kannan
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引用次数: 1
Antipalindromic numbers Antipalindromic数字
Pub Date : 2020-08-16 DOI: 10.14311/ap.2021.61.0428
L'ubomíra Dvoráková, Stanislav Kruml, David Ryzak
Everybody has certainly heard about palindromes: words that stay the same when read backwards. For instance kayak, radar, or rotor. Mathematicians are interested in palindromic numbers: positive integers whose expansion in a certain integer base is a palindrome. The following problems are studied: palindromic primes, palindromic squares and higher powers, multibased palindromic numbers, etc. In this paper, we define and study antipalindromic numbers: positive integers whose expansion in a certain integer base is an antipalindrome. We present new results concerning divisibility and antipalindromic primes, antipalindromic squares and higher powers, and multibased antipalindromic numbers. We provide a user-friendly application for all studied questions.
每个人都听说过回文:倒读时保持不变的单词。例如皮艇,雷达,或转子。数学家对回文数很感兴趣:回文数是正整数,它在一定的整数基数上展开是回文。研究了回文素数、回文平方数和回文幂数、多基回文数等问题。本文定义并研究了反回文数:在一定整数基数上展开为反回文数的正整数。我们提出了关于可除性和反回文质数,反回文平方和更高幂,以及多基反回文数的新结果。我们为所有研究过的问题提供了一个用户友好的应用程序。
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引用次数: 1
Combinatorics of Multicompositions 多重组合学
Pub Date : 2020-08-11 DOI: 10.1007/978-3-030-67996-5_16
Brian Hopkins, S. Ouvry
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引用次数: 4
Coloring the normalized Laplacian for oriented hypergraphs 有向超图的规格化拉普拉斯的上色
Pub Date : 2020-08-07 DOI: 10.1016/j.laa.2021.07.018
A. Abiad, R. Mulas, Dong Zhang
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引用次数: 6
Bordered Complex Hadamard Matrices and Strongly Regular Graphs 有边复Hadamard矩阵与强正则图
Pub Date : 2020-08-03 DOI: 10.4036/IIS.2020.R.03
Takuya Ikuta, A. Munemasa
We consider bordered complex Hadamard matrices whose core is contained in the Bose-Mesner algebra of a strongly regular graph. Examples include a Butson-type complex Hadamard matrix whose core is contained in the Bose-Mesner algebra of a conference graph due to J. Wallis, and a family of Hadamard matrices given by Singh and Dubey. In this paper, we show that there is also a non Butson-type complex Hadamard matrix whose core is contained in the Bose-Mesner algebra of a conference graph, and prove that there are no other bordered complex Hadamard matrices whose core is contained in the Bose-Mesner algebra of a strongly regular graph.
考虑核包含在强正则图的Bose-Mesner代数中的有边复Hadamard矩阵。例子包括一个核心包含在J. Wallis会议图的Bose-Mesner代数中的butson型复Hadamard矩阵,以及Singh和Dubey给出的一类Hadamard矩阵。本文证明了在会议图的Bose-Mesner代数中也存在一个核包含在非butson型复Hadamard矩阵,并证明了在强正则图的Bose-Mesner代数中不存在其他有边复Hadamard矩阵的核包含在其上。
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引用次数: 0
On the modular Jones polynomial 在琼斯模多项式上
Pub Date : 2020-07-31 DOI: 10.5802/crmath.106
G. Pagel
A major problem in knot theory is to decide whether the Jones polynomial detects the unknot. In this paper we study a weaker related problem, namely whether the Jones polynomial reduced modulo an integer $n$ detects the unknot. The answer is known to be negative for $n=2^k$ with $kgeq 1$ and $n=3$. Here we show that if the answer is negative for some $n$, then it is negative for $n^k$ with any $kgeq 1$. In particular, for any $kgeq 1$, we construct nontrivial knots whose Jones polynomial is trivial modulo~$3^k$.
结理论中的一个主要问题是确定琼斯多项式是否检测到解结。本文研究了一个较弱的相关问题,即琼斯多项式对整数的约模$n$是否检测到解结。已知对于$n=2^k$、$kgeq 1$和$n=3$,答案是否定的。这里我们表明,如果对于某个$n$的答案是负的,那么对于任何$kgeq 1$的$n^k$的答案都是负的。特别地,对于任意$kgeq 1$,我们构造其琼斯多项式为平凡模$3^k$的非平凡结。
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引用次数: 0
On a Zero-Sum Problem Arising From Factorization Theory 论因式分解理论带来的零和问题
Pub Date : 2020-07-20 DOI: 10.1007/978-3-030-67996-5_2
Aqsa Bashir, A. Geroldinger, Qinghai Zhong
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引用次数: 0
ON THE DOT PRODUCT GRAPH OF A COMMUTATIVE RING II 交换环的点积图
Pub Date : 2020-07-14 DOI: 10.24330/ieja.768135
M. Abdulla, Ayman Badawi
In 2015, the second-named author introduced the dot product graph associated to a commutative ring A. Let A be a commutative ring with nonzero identity, 1 ≤ n < ∞ be an integer, and R = A × A × · · · × A (n times). We recall that the total dot product graph of R is the (undirected) graph TD(R) with vertices R∗ = R {(0, 0, ...,0)}, and two distinct vertices x and y are adjacent if and only if x · y = 0 ∈ A (where x · y denotes the normal dot product of x and y). Let Z(R) denote the set of all zero-divisors of R. Then the zero-divisor dot product graph of R is the induced subgraph ZD(R) of TD(R) with vertices Z(R) = Z(R){(0, 0, ..., 0)}. Let U(R) denote the set of all units of R. Then the unit dot product graph of R is the induced subgraph UD(R) of TD(R) with vertices U(R). In this paper, we study the structure of TD(R), UD(R), and ZD(R) when A = Zn or A = GF (pn), the finite field with pn elements, where n ≥ 2 and p is a prime positive integer. 1991 Mathematics Subject Classification Primary: 13A15; Secondary: 13B99; 05C99
2015年,第二位作者引入了可交换环a的点积图,设a为非零单位元的可交换环,1≤n <∞为整数,R = a × a ×···× a (n次)。我们回想一下,总点积图的R(无向)图TD (R)与顶点∗= R {}(0, 0,…,0),和两个不同的顶点x和y是相邻当且仅当x·y = 0∈(x·y表示x和y的正常点积)。让Z (R)表示的所有zero-divisors R R的零因子图点积是诱导子图ZD (R)的TD (R)与顶点Z (R) = Z (R) {(0, 0,…, 0)}。设U(R)表示R的所有单位的集合,则R的单位点积图就是TD(R)的引子图UD(R),其顶点为U(R)。本文研究了具有pn元的有限域中,当n≥2且p为素数正整数时,当A = Zn或A = GF (pn)时,TD(R)、UD(R)和ZD(R)的结构。1991年数学学科分类小学:13A15;二级:13 b99;05年c99
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引用次数: 0
Polynomials related to chromatic polynomials 与色多项式相关的多项式
Pub Date : 2020-07-10 DOI: 10.1142/9789812569462_0011
F. Dong
For a simple graph $G$, let $chi(G,x)$ denote the chromatic polynomial of $G$. This manuscript introduces some polynomials which are related to chromatic polynomial and their relations.
对于一个简单图$G$,设$chi(G,x)$表示$G$的色多项式。本文介绍了一些与色多项式有关的多项式及其相互关系。
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引用次数: 0
Matchings in regular graphs: minimizing the partition function 正则图中的匹配:最小化配分函数
Pub Date : 2020-06-30 DOI: 10.22108/TOC.2020.123763.1742
M'arton Borb'enyi, P'eter Csikv'ari
For a graph $G$ on $v(G)$ vertices let $m_k(G)$ denote the number of matchings of size $k$, and consider the partition function $M_{G}(lambda)=sum_{k=0}^nm_k(G)lambda^k$. In this paper we show that if $G$ is a $d$--regular graph and $0 frac{1}{v(K_{d+1})}ln M_{K_{d+1}}(lambda).$$ The same inequality holds true if $d=3$ and $lambda<0.3575$. More precise conjectures are also given.
对于一个图$G$在$v(G)$顶点上,设$m_k(G)$表示大小$k$的匹配个数,并考虑配分函数$M_{G}(lambda)=sum_{k=0}^nm_k(G)lambda^k$。本文证明了$G$是$d$-正则图,且$0 frac{1}{v(K_{d+1})}ln M_{K_{d+1}}(lambda)。如果$d=3$和$lambda<0.3575$,同样的不等式成立。还给出了更精确的推测。
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引用次数: 1
期刊
arXiv: Combinatorics
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