环F_3+uF_3+vF_3+uvF_3上的循环码

研究了环R=F_3+uF_3+vF_3+uvF_3上循环码的结构(u~2=u,v~2=v,uu=uu),证明了该环上的循环码是主理想生成的,并给出了其上循环码的生成多项式.     

3-Kings in 3-partite tournaments

We present all possible distributions of 3-kings in 3-partite tournaments with at most one transmitter.     

L'équation ξ3 + η3 + ζ3 = 0 et la courbex 3+y 3=1

Sans résumé     

Finding Δ(Σ) for a surface σ of characteristic χ(Σ) = −5

For each surface Σ, we define Δ(Σ) = max{Δ(G)|Gis a class two graph of maximum degree Δ(G) that can be embedded in Σ}. Hence, Vizing's Planar Graph Conjecture can be restated as Δ(Σ) = 5 if Σ is a plane. In this paper, we show that Δ(Σ) = 9 if Σ is a surface of characteristic χ(Σ) = ?5. © 2010 Wiley Periodicals, Inc. J Graph Theory 68:148‐168, 2011     

The denormalized 3×3 lemma

The classical 3×3 lemma holds in any regular protomodular category with a zero object. It is investigated here whether there is a “denormalized” version when the category no longer has a zero object, as, for instance, any slice category of the category , or any slice category of an abelian category. The answer is actually positive in the weaker context of regular Mal'cev categories.     

Bordeaux 3-color conjecture and 3-choosability

A graph G=(V,E) is list L-colorable if for a given list assignment L={L(v):v∈V}, there exists a proper coloring c of G such that c(v)∈L(v) for all v∈V. If G is list L-colorable for every list assignment with |L(v)|?k for all v∈V, then G is said to be k-choosable.In this paper, we prove that (1) every planar graph either without 4- and 5-cycles, and without triangles at distance less than 4, or without 4-, 5- and 6-cycles, and without triangles at distance less than 3 is 3-choosable; (2) there exists a non-3-choosable planar graph without 4-cycles, 5-cycles, and intersecting triangles. These results have some consequences on the Bordeaux 3-color conjecture by Borodin and Raspaud [A sufficient condition for planar graphs to be 3-colorable. J. Combin. Theory Ser. B 88 (2003) 17-27].     

D-modules associated to 3×3 matrices

We classify regular holonomic $\text{D}$-modules whose characteristic variety is contained in the union of conormal bundles to the orbits of the group of invertible matrices. The main result is an equivalence between the category of such $\text{D}$-modules and the one of graded modules of finite type over a Weyl algebra. To cite this article: P. Nang, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

A 3-Local Characterization of M12 and SL3(3)

We identify the sporadic simple group M₁₂ and the simple group SL₃(3) from some part of their 3-local structure. We also present a graph theoretic analogue of our main theorem. Received: 6 October 2008, Revised: 25 October 2008     

Family of Pearson discrete distributions generated by the univariate hypergeometric function 3F2(α1, α2, α3; γ1, γ2; λ)

In this work we present a study of the Pearson discrete distributions generated by the hypergeometric function ₃F₂(α₁, α₂, α₃;γ₁, γ₂; λ), a univariate extension of the Gaussian hypergeometric function, through a constructive methodology. We start from the polynomial coefficients of the difference equation that lead to such a function as a solution. Immediately after, we obtain the generating probability function and the differential equation that it satisfies, valid for any admissible values of the parameters. We also obtain the differential equations that satisfy the cumulants generating function, moments generating function and characteristic function, From this point on, we obtain a relation in recurrences between the moments about the origin, allowing us to create an equation system for estimating the parameters by the moment method. We also establish a classification of all possible distributions of such type and conclude with a summation theorem that allows us study some distributions belonging to this family. © 1997 by John Wiley & Sons, Ltd.     

SL(3,3~n)和SU(3,3~n)的第一Cartan不变量

确定Cartan不变量是代数群与相关的李型有限群的模表示理论中的一个重要方面.作者利用代数群模表示理论中的一系列结果,计算了3~n个元素的有限域上特殊线性群SL(3,3~n)和特殊酉群SU(3,3~n)的第一Cartan不变量,得到如下结论:当G=SL(3,3~n)时,C_(00)~((n))=a~n+b~n+6~n-2·8~n;而当G=SU(3,3~n)时,C_(00)~((n))=a~n+b~n+6~n-2·8~n+2·(1+(-1)~n),其中a,b是多项式x~2-20x+48的两个根.另外,作者也得到了射影不可分解模U_n(0,0)的维数公式:dim U_n(0,0)=(12~n-6~n+∈)·3~(3n),其中,当G=SL(3,3~n)时,∈=1;而当G=SU(3,3~n)时,∈=-1.     

Möbiussche Tetraeder und SegrescheV 3 3

Ohne Zusammenfassung     

Unsolvability in 3 × 3 Matrices

A set of 3 × 3 matrices over the integers will be said to be mortal if the zero matrix can be expressed as a finite product of members of the set. It is shown in this paper that the problem of deciding whether a given finite set is mortal is recursively unsolvable.     

Metric packing for K 3+K 3

In this paper, we consider the metric packing problem for the commodity graph of disjoint two triangles K ₃+K ₃, which is dual to the multiflow feasibility problem for the commodity graph K ₃+K ₃. We prove a strengthening of Karzanov’s conjecture concerning quarterintegral packings by certain bipartite metrics.     

三阶矩阵的平方根

给出3×3矩阵的平方根公式，并通过实例阐明我们的方法，完善了有关文献中的某些结果．     

3g3维半单Hopf代数的结构

设g为素数,k是特征为零的代数闭域,日是k上的3q3维半单Hopf代数．本文证明了日总是半可解的,即H可由群代数或对偶群代数经过扩张得到．