共查询到19条相似文献,搜索用时 78 毫秒
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本文给出如下结果: 定理当m为偶数时,当m为奇数时, 其中L_n,C_m分别是阶为n和m的路径和圈,且n≥2,m≥3。设且。未加说明的术语和符号同[1]、[2]。 相似文献
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基于矩阵运算,给出任意双偶数阶和非素数阶幻方的新构造方法:1)由任一低阶m(m为偶数且m≠2)幻方生成一高阶2m阶幻方;2)利用已知的m(m≠2)阶和n(n≠2)阶两个幻方,构造任意的非素数mn阶幻方,加强一些条件后,进一步提出构造两类高级幻方(泛对角线幻方和关联幻方)的新方法. 相似文献
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设W(m,n)是特征p3的代数闭域上有限维Witt型李超代数.证明了W(m,n)的极大根阶化子代数一定是其极大Z-阶化子代数,从而刻画了W(m,n)的所有极大根阶化子代数.结果有助于理解Witt型李超代数W(m,n)的内在性质. 相似文献
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对称正交反对称矩阵反问题解存在的条件 总被引:25,自引:1,他引:24
戴华 《高等学校计算数学学报》2002,24(2):169-178
矩阵反问题和矩阵特征值反问题在科学和工程技术中具有广泛的应用,有关它们的研究已取得了许多进展[1,2].[3]和[4]分别研究了反对称矩阵反问题和双反对称矩阵特征值反问题等.本文研究一类更广泛的对称正交反对称矩阵反问题.用Rn×m(Cn×m)表示n×m实(复)矩阵的全体,ASRn×n表示n阶反对称矩阵的全体,ABSRn×n表示n阶双反对称矩阵的全体,ORn×n表示n阶正交矩阵的全体.A+表示矩阵A的Moore-Penrose广义逆.In表示n阶单位矩阵.ei表示n阶单位矩阵的第i列,Sn=[en,en-1, 相似文献
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1引言令R~(n×m)、OR~(n×n)、SR~(n×n)(SR_0~(n×n))分别表示所有n×m阶实矩阵、n阶实正交阵、n阶实对称矩阵(实对称半正定阵)的全体,A~ 表示A的Moore-Penrose广义逆,I_k表示k阶单位矩阵,S_k表示k阶反序单位矩阵。R(A)表示A的列空间,N(A)表示A的零空间,rank(A)表示矩阵A的秩。对A=(a_(ij)),B=(b_(ij))∈R~(n×m),A*B表示A与 相似文献
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设A是m×n阶复矩阵,分解式A=QH称为A的广义极分解,如果Q是m×n阶次酉短阵和H是n×n半正定的Hermite矩阵.本文给出了广义极分解的一些性质和推广了有关近似极因子的相关结论. 相似文献
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给出2k维m阶t次幻方及m模方阵,m模列满秩矩阵,模线,m经典模线集和t次m模基因阵的概念,并用矩阵法和组合法初步研究了t次幻方特别是三次幻方的构作.证明:(i)若存在2k阶t次m模基因阵,则存在2k维m阶t次幻方;(ii)若N=P1α1P2α2…PSαS为N的标准分解式,iα≥3,Piiα≥16(1≤i≤S),则存在二维N阶三次幻方;(iii)若存在二维偶m阶2t+1次幻方和二维n阶2t次幻方,则存在二维mn阶2t+1次幻方;(iv)若存在二维m阶和n阶t次幻方,则存在二维mn阶t次幻方;(v)当t≥3时,不存在二维单偶数阶t次幻方. 相似文献
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The constructional methods of pandiagonal snowflake magic squares of orders 4m are established in paper [3]. In this paper, the constructional methods of pandiagonal snowflake magic squares of odd orders n are established with n = 6m l, 6m 5 and 6m 3, m is an odd positive integer and m is an even positive integer 9|6m 3. It is seen that the number sets for constructing pandiagonal snowflake magic squares can be extended to the matrices with symmetric partial difference in each direction for orders 6m 1 , 6m 5; to the trisection matrices with symmetric partial difference in each direction for order 6m 3. 相似文献
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A latin square is a bachelor square if it does not possess an orthogonal mate; equivalently, it does not have a decomposition
into disjoint transversals. We define a latin square to be a confirmed bachelor square if it contains an entry through which there is no transversal. We prove the existence of confirmed bachelor squares for all
orders greater than three. This resolves the existence question for bachelor squares. 相似文献
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We (1) determine the number of Latin rectangles with 11 columns and each possible number of rows, including the Latin squares
of order 11, (2) answer some questions of Alter by showing that the number of reduced Latin squares of order n is divisible by f! where f is a particular integer close to
(3) provide a formula for the number of Latin squares in terms of permanents of (+1, −1)-matrices, (4) find the extremal
values for the number of 1-factorisations of k-regular bipartite graphs on 2n vertices whenever 1 ≤ k ≤ n ≤ 11, (5) show that the proportion of Latin squares with a non-trivial symmetry group tends quickly to zero as the order
increases.
Received September 3, 2004 相似文献
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Two identities are obtained by Jacobi‘s triple product identity and some basic operators.By applying these identities,Jacobi‘s theorem for the number of representations of an integer as a sum of eight squares is easily proved. 相似文献
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讨论不完全自正交拉丁方ISOLS(v;3,3)的存在性问题.证明当v≥12,v{13,14,15,16,17,18,19,20,21,22,23,24,25,27,28,29,30,31,33,35,36}时,存在ISOLS(v;3,3). 相似文献