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1.
We give a Grobner-Shirshov basis of quantum group of type F4 by using the Ringel-Hall algebra approach. We compute all skew-commutator relations between the isoclasses of indecomposable representations of Ringel- Hall algebras of type F4 by using an 'inductive' method. Precisely, we do not use the traditional way of computing the skew-commutative relations, that is first compute all Hall polynomials then compute the corresponding skew- commutator relations; instead, we compute the 'easier' skew-commutator relations which correspond to those exact sequences with middle term indecomposable or the split exact sequences first, then 'deduce' others from these 'easier' ones and this in turn gives Hall polynomials as a byproduct. Then using the composition-diamond lemma prove that the set of these relations constitute a minimal CrSbner-Shirshov basis of the positive part of the quantum group of type F4. Dually, we get a Grobner-Shirshov basis of the negative part of the quantum group of type F4. And finally, we give a Gr6bner-Shirshov basis for the whole quantum group of type F4.  相似文献   

2.
Let v be a positive integer and let K be a set of positive integers. A (v, K, 1)-Mendelsohn design, which we denote briefly by (v, K, 1)-MD, is a pair (X, B) where X is a v-set (of points) and B is a collection of cyclically ordered subsets of X (called blocks) with sizes in the set K such that every ordered pair of points of X are consecutive in exactly one block of B. If for all t =1, 2,..., r, every ordered pair of points of X are t-apart in exactly one block of B, then the (v, K, 1)-MD is called an r-fold perfect design and denoted briefly by an r-fold perfect (v, K, 1)-MD. If K = {k) and r = k - 1, then an r-fold perfect (v, (k), 1)-MD is essentially the more familiar (v, k, 1)-perfect Mendelsohn design, which is briefly denoted by (v, k, 1)-PMD. In this paper, we investigate the existence of 4-fold perfect (v, (5, 8}, 1)-Mendelsohn designs.  相似文献   

3.
Let Aut. (X) denote the group of homotopy classes of self-homotopy equivalences of X, which induce identity automorphisms of homology group. We describe a decomposition of Aut. (X1 V…VXn) as a product of its simpler subgroups. We consider the subgroup Aut∑(X) of all self homotopy classes α of X such that ∑α=1∑X: ∑X → ∑X, and also give some properties of Aut∑(X).  相似文献   

4.
L(j,k)-number of Direct Product of Path and Cycle   总被引:1,自引:0,他引:1  
For positive numbers j and k, an L(j,k)-labeling f of G is an assignment of numbers to vertices of G such that |f(u)-f(v)|≥j if uv∈E(G), and |f(u)-f(v)|≥k if d(u,v)=2. Then the span of f is the difference between the maximum and the minimum numbers assigned by f. The L(j,k)-number of G, denoted by λj,k(G), is the minimum span over all L(j,k)-labelings of G. In this paper, we give some results about the L(j,k)-number of the direct product of a path and a cycle for j≤k.  相似文献   

5.
完全图K_n(n为奇数)或K_n-I(n为偶数,I为K_n的1-因子)是否有2-因子分解称Oberwolfach问题.每个2-因子恰包含α_i个长为m_i的圈(i=1,2,…,t)的Oberwolfach问题记为OP(m_1~(α_1),m_2~(α_2),…,m_t~(α_t)).证明了对任意的a≥0,b=2,3和s=3,5,6,且(a,s,b)≠(0,3,2),都存在OP(4~a,s~b)的解.  相似文献   

6.
The present paper deals with the gracefulness of unconnected graph (jC_(4n))∪P_m,and proves the following result:for positive integers n,j and m with n≥1,j≥2,the unconnected graph(jC_(4n))∪P_m is a graceful graph for m=j-1 or m≥n+j,where C_(4n) is a cycle with 4n vertexes,P_m is a path with m+1 vertexes,and(jC_(4n))∪P_m denotes the disjoint union of j-C_(4n) and P_m.  相似文献   

7.
自 1992 年 Gronau 和 Mullin 提出超单设计的概念以来, 很多研究者参与了超单设计的研究. 超单设计在编码等方面也有广泛的应用. 超单可分组设计是超单设计的重要组成部分. 本文我们主要研究区组大小为4 的二重超单可分解的可分组设计, 并基本解决了此类设计的存在性问题.  相似文献   

8.
本文提出了构造群GF(p)及GF(p~e)上的一类ARBIBD的简单而有效的算法。它们易于计算机和手工生成,且可用来推广复数旋转码及加速编码速度。  相似文献   

9.
On the Geometry of the (1, 1)-Tensor Bundle with Sasaki Type Metric   总被引:1,自引:1,他引:1  
Curvature properties are studied for the Sasaki metric on the (1,1) tensor bundle of a Riemannian manifold. As an application, examples of almost para-Nordenian and para-K(a)hler-Nordenian B-metrics are constructed on the (1,1) tensor bundle by looking at the Sasaki metric. Also, with respect to the para-Nordenian B-structure, paraholomorphic conditions for the complete lifts of vector fields are analyzed.  相似文献   

10.
Let D be a 2-(v, k, 4) symmetric design and G be a flag-transitive point-primitive automorphism group of D with XGAut(X) where XPSL 2(q). Then D is a 2-(15, 8, 4) symmetric design with X = PSL 2(9) and X x = PGL 2(3) where x is a point of D.  相似文献   

11.
H. Cao  F. Yan 《Discrete Mathematics》2009,309(16):5111-5119
In this paper, we investigate the existence of a super-simple (4, 5)-GDD of type gu and show that such a design exists if and only if u≥4, g(u−2)≥10, and .  相似文献   

12.
《Discrete Mathematics》2022,345(11):112983
We determine the 22 isomorphism classes of 4-GDDs with group type 3562 and compare their automorphism groups. We also observe for the first time an example of a three dimensional Pasch triangle in a GDD.  相似文献   

13.
14.
15.
Group divisible designs (GDDs) with block size 4 and at most 30 points are known for all feasible group types except three, namely 2 3 5 4 , 3 5 6 2 , and 2 2 5 5 . In this paper we provide solutions for the first two of these three 4‐GDDs without assuming any automorphisms. We also construct several other 4‐GDDs. These include classes of 4‐GDDs of types ( 3 m ) 4 ( 6 m ) q ( 3 n ) 1 for 0 n ( q + 1 ) m where q { 2 , 3 } and solutions for 4‐GDDs of types 3 t 6 s for a wide range of values of s 2 , t 4 satisfying t 0 or 1 ( mod 4 ) , including all cases with 4 t s ? 1 . Most of the remaining unknown 4‐GDDs of type 3 t 6 s have ( s ? 1 ) < t < 2 ( s ? 1 ) .  相似文献   

16.
In this article, we construct group divisible designs (GDDs) with block size five, group-type gu and index unity. The necessary condition for the existence of such a GDD is u ≷ 5, (u - 1)g ≡ 0 (mod 4) and u(u - 1)g2 ≡ 0 (mod 20). It is shown that these necessary conditions are also sufficient, except possibly in a few cases. Additionally, a new construction to obtain GDDs using holey TDs is presented. © 1997 John Wiley & Sons, Inc. J Combin Designs 5: 275–299, 1997  相似文献   

17.
《组合设计杂志》2018,26(11):519-539
Building upon the work of Wei and Ge (Designs, Codes, and Cryptography 74, 2015), we extend the range of positive integer parameters g, u, and m for which group divisible designs with block size 4 and type are known to exist. In particular, we show that the necessary conditions for the existence of these designs when and are sufficient in the following cases: , with one exception, 2651, , and .  相似文献   

18.
19.
Super-simple designs are useful in constructing codes and designs such as superimposed codes and perfect hash families. In this article, we investigate the existence of a super-simple (ν, 5, 5) balanced incomplete block design and show that such a design exists if and only if ν ≡ 1 (mod 4) and ν ≥ 17 except possibly when ν = 21. Applications of the results to optical orthogonal codes are also mentioned. Research supported by NSERC grant 239135-01.  相似文献   

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