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《Discrete Mathematics》1986,62(2):197-210
A Kirkman square with index λ, latinicity μ, block size k and v points, KSk(v; μ, λ), is a t × t array (t = λ(v − 1)/μ(k − 1)) defined on a v-set V such that (1) each point of V is contained in precisely μ cells of each row and column, (2) each cell of the array is either empty or contains a k subset of V, and (3) the collection of blocks obtained from the nonempty cells of the array is a (v, k, λ)-BIBD. The existence question for KS2(v; μ, λ) has been completely selttled. We are interested in the next case k = 3. The case k = 3 and μ = λ = 1 appears to be quite difficult, although some existence results are available. For λ > 1 and μ ⩾ 1, the problem is more tractable. In this paper, we prove the existence of KS3(v; 2, 4) for v ≡ 3 (mod 12), v ≡ 6 (mod 60) and v ≡ 9 (mod 96). 相似文献
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Xiao Xia ZHANG 《数学学报(英文版)》2006,22(4):1221-1226
In this paper, we first prove that the θ-deformation Uθ(2) of U(2) constructed by Connes and Violette is our special case of the quantum group Uq(2) constructed in our previous paper. Then we will show that the set of truces on the C^* -algebra Uθ, θ irrational, is determined by the set of the truces on a subalgebra of Uθ. 相似文献
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R. Julian R. Abel Norman J. Finizio Malcolm Greig Luis B. Morales 《Designs, Codes and Cryptography》2009,51(1):79-97
(2, 8) Generalized Whist tournament Designs (GWhD) on v players exist only if . We establish that these necessary conditions are sufficient for all but a relatively small number of (possibly) exceptional
cases. For there are at most 12 possible exceptions: {177, 249, 305, 377, 385, 465, 473, 489, 497, 537, 553, 897}. For there are at most 98 possible exceptions the largest of which is v = 3696. The materials in this paper also enable us to obtain four previously unknown (4, 8)GWhD(8n+1), namely for n = 16,60,191,192 and to reduce the list of unknown (4, 8) GWhD(8n) to 124 values of v the largest of which is v = 3696.
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In this article, we verify Dade's projective invariant conjecture for the symplectic group Sp4(2 n ) and the special unitary group SU4(22n ) in the defining characteristic, that is, in characteristic 2. Furthermore, we show that the Isaacs–Malle–Navarro version of the McKay conjecture holds for Sp4(2 n ) and SU4(22n ) in the defining characteristic, that is, Sp4(2 n ) and SU4(22n ) are good for the prime 2 in the sense of Isaacs, Malle, and Navarro. 相似文献
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We prove that the set of non-pseudo-Anosov elements in the Torelli group is exponentially small. This answers a question of Kowalski (2008). 相似文献
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Donal O’Regan 《Rendiconti del Circolo Matematico di Palermo》2009,58(1):87-97
A number of new Lefschetz fixed point theorems are established for ANES(compact) maps. Also compact absorbing contraction
maps are discussed.
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Jiang Jiahe 《数学学报(英文版)》1988,4(3):234-241
The present paper is the continuation of [1]. Some further generalizations of the fixed point theorems in [2] are obtained
by means of the results in [1].
Project supported by the National Natural Science Foundation of China 相似文献
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文章研究了环R=F_4[v]/(v~2+v)上的DNA码.基于环R上长度为n的线性码的代数结构,给出了环R上长度为n的线性码是可逆的DNA码的一个充要条件.同时,给出了环R上长度为n的线性码是可逆补DNA码的一个充要条件. 相似文献
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An S(2, 4, v) design has a type B χ‐coloring if it is possible to assign one of χ colors to each point such that each block contains three points of one color and one point of a different color, and all χ colors are used. In this article we describe the constructions of type B χ‐colorable S(2, 4, v)s for (v, χ) = (61, 3), (100, 2) and (109, 3), and we give a new general construction. © 2007 Wiley Periodicals, Inc. J Combin Designs 15: 357–368, 2007 相似文献
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It is shown that the necessary condition for a given Sλ(2,4,u) to be embedded in some Sλ(2,4,v) as a subdesign, namely v ≥ 3u + 1, is also sufficient for the case of λ = 6. Combining this with the previously known results gives the same sufficiency for any positive integer λ. © 1994 John Wiley & Sons, Inc. 相似文献
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G. B. Podkolzin 《Ukrainian Mathematical Journal》1990,42(3):380-382
Two infinitesimal objects are constructed for the hypercomplex system with base SO(4)//SO(2). It is proved that they are finitely generated algebras. Generators are found for both algebras and commutation relations between the generators established in each case. It is proved that these algebras are of the Poincaré -Birkhoff-Witt type.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 3, pp. 427–429, March, 1990. 相似文献
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good morning, Daisy. In 2027, your Development Committee approached me with a curious proposal. You, a dynamic AI system,
were soon to be launched, and to demonstrate your capability to discover new mathematics with a minimum of instruction, they
wanted a beginner’s course in elementary group theory (meant for 相似文献
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《数学的实践与认识》2015,(9)
设G为有限群,且满足M(G)=M(F4(2~n)),n1.则G有正规子群同构于F_4(2~n).特别地,若|G|=|F_4(2~n)|,则G≌F_4(2~n). 相似文献
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本文证明了当2-((u),κ,1)设计的自同构群G的基柱soc(G)=2F4(q2)时,Buekenhaut-Delandtsheer-Doyen猜想成立,即自同构群G的基柱为Ree群2F4(q2)的区本原2-((u),k,1)设计必为点本原的. 相似文献
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A (v,k,t) trade T=T
1−T
2 of volume m consists of two disjoint collections T
1 and T
2 each containing m blocks (k-subsets) such that each t-subset is contained in the same number of blocks in T
1 and T
2. If each t-subset occurs at most once in T
1, then T is called a Steiner (k,t) trade. In this paper, we continue our investigation of the spectrum S(k,2); that is, the set of allowable volumes of Steiner (k,t) trades when t=2. By using the concept of linked trades, we show that 2k+1∈S(k,2) precisely when k∈{3, 4, 7}.
Received: February 28, 1997 相似文献
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本文证明了当2-(v,k,1)设计的自同构群G的基柱soc(G)=2F4(q2)时,Buekenhaut-Delandtsheer-Doyen猜想成立,即自同构群G的基柱为Ree群2F4(q2)的区本原2-(v,k,1)设计必为点本原的. 相似文献