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1.
刘颖  马红平  苗正科 《东北数学》2008,24(4):311-318
For a symmetric sign pattern S1 the inertia set of S is defined to be the set of all ordered triples si(S) = {i(A) : A = A^T ∈ Q(S)} Consider the n × n sign pattern Sn, where Sn is the pattern with zero entry (i,j) for 1 ≤ i = j ≤ n or|i -j|=n- 1 and positive entry otherwise. In this paper, it is proved that si(Sn) = {(n1, n2, n - n1 - n2)|n1≥ 1 and n2 ≥ 2} for n ≥ 4.  相似文献   

2.
Let S belong to Zn-{0}.The circulant digraph DCn(S) is a directed graph with vertex set Zn and are set {(i,i s):i∈Zn,s∈S},A.Adam conjectured that DCn(S)≌DCn(T) if and only if T=uS for some unit u mod n.In this paper we prove that the conjecture is true if S is a minimal generating set of Zn and thus determine the full automorphism groups of such digraphs.The methods we employ are new and easy to be understood.  相似文献   

3.
Let N denote the set of all nonnegative integers and A be a subset of N.Let W be a nonempty subset of N.Denote by F~*(W) the set of all finite,nonempty subsets of W.Fix integer g≥2,let A_g(W) be the set of all numbers of the form sum f∈Fa_fg~f where F∈F~*(W)and 1≤a_f≤g-1.For i=0,1,2,3,let W_i = {n∈N|n≡ i(mod 4)}.In this paper,we show that the set A = U_i~3=0 A_g(W_i) is a minimal asymptotic basis of order four.  相似文献   

4.
For a graph G =(V,E),a subset VS is a dominating set if every vertex in V is either in S or is adjacent to a vertex in S.The domination number γ(G) of G is the minimum order of a dominating set in G.A graph G is said to be domination vertex critical,if γ(G-v) γ(G) for any vertex v in G.A graph G is domination edge critical,if γ(G ∪ e) γ(G) for any edge e ∈/E(G).We call a graph G k-γ-vertex-critical(resp.k-γ-edge-critical) if it is domination vertex critical(resp.domination edge critical) and γ(G) = k.Ananchuen and Plummer posed the conjecture:Let G be a k-connected graph with the minimum degree at least k+1,where k 2 and k≡|V|(mod 2).If G is 3-γ-edge-critical and claw-free,then G is k-factor-critical.In this paper we present a proof to this conjecture,and we also discuss the properties such as connectivity and bicriticality in 3-γ-vertex-critical claw-free graph.  相似文献   

5.
It is shown that for any directed quasi ordered set (Q,≤),there is a minimal ordinal number λ such that every cofinal subset of Q contains a cofinal subset which is the o-th class original set of a λ-th class chain of Q. A special case of our results gives necessary and sufficient conditions for a directed set to contain a cofinal chain.  相似文献   

6.
三幂等符号模式矩阵的结构   总被引:2,自引:0,他引:2  
Abstract. A matrix whose entries are , -, and 0 is called a sign pattern matrix. For a signpattern matrix A,if A3 =A, then A is said to be sign tripotent. In this paper, the characteriza-tion of the n by n(n≥2) sign pattern matrices A which are sign tripotent has been given out.Furthermore, the necessary and sufficient condition of A3=A but A2≠A is obtained, too.  相似文献   

7.
Let G be a finite group. A nonempty subset X of G is said to be noncommuting if xy≠yx for any x, y ∈ X with x≠y. If |X| ≥ |Y| for any other non-commuting set Y in G, then X is said to be a maximal non-commuting set. In this paper, we determine upper and lower bounds on the cardinality of a maximal non-commuting set in a finite p-group with derived subgroup of prime order.  相似文献   

8.
Let n and k(n ≥ k 〉 1) be two non-negative integers.A k-multi-hypertournament on n vertices is a pair(V,A),where V is a set of vertices with |V|=n,and A is a set of k-tuples of vertices,called arcs,such that for any k-subset S of V,A contains at least one(at most k!) of the k! k-tuples whose entries belong to S.The necessary and suffcient conditions for a non-decreasing sequence of non-negative integers to be the out-degree sequence(in-degree sequence) of some k-multi-hypertournament are given.  相似文献   

9.
In the combinatorial geometry of convex sets the question of how efficiently a family of convex sets can be pierced by points has led to various problems which may be regarded as extensions of the Helly-type problems. A family of sets is said to be n-pierceable (abbreviated as Пn) if there exists a set of n points such that each member of the family contains at least one of them. A family of sets is said to be Пnk if every subfamily of size k or less is Пn. The famous Helly theorem in combinatorial geometry asserts that for finite families of convex sets in the plane П13 implies П1. In a recent paper by M. Katchalski and D. Nashtir[a] the following conjecture of Griinbaum[2] was mentioned again:  相似文献   

10.
Let G be a nontrivial connected and vertex-colored graph. A subset X of the vertex set of G is called rainbow if any two vertices in X have distinct colors. The graph G is called rainbow vertex-disconnected if for any two vertices x and y of G, there exists a vertex subset S of G such that when x and y are nonadjacent, S is rainbow and x and y belong to different components of G-S; whereas when x and y are adjacent, S + x or S + y is rainbow and x and y belong to different components of(G-xy)-S. For a connected graph G, the rainbow vertex-disconnection number of G, denoted by rvd(G), is the minimum number of colors that are needed to make G rainbow vertexdisconnected. In this paper, we characterize all graphs of order n with rainbow vertex-disconnection number k for k ∈ {1, 2, n}, and determine the rainbow vertex-disconnection numbers of some special graphs. Moreover, we study the extremal problems on the number of edges of a connected graph G with order n and rvd(G) = k for given integers k and n with 1 ≤ k ≤ n.  相似文献   

11.
The concept of a critical set of refined inertias for an irreducible zero–nonzero pattern is defined, and all minimal critical sets of refined inertias for irreducible zero–nonzero patterns of orders 2 and 3 are identified. As an application of these results, a new method is used to identify all minimal critical sets of inertias for irreducible zero–nonzero patterns of orders 2 and 3.  相似文献   

12.
符号图$S=(S^u,\sigma)$是以$S^u$作为底图并且满足$\sigma: E(S^u)\rightarrow\{+,-\}$. 设$E^-(S)$表示$S$的负边集. 如果$S^u$是欧拉的(或者分别是子欧拉的, 欧拉的且$|E^-(S)|$是偶数, 则$S$是欧拉符号图(或者分别是子欧拉符号图, 平衡欧拉符号图). 如果存在平衡欧拉符号图$S''$使得$S''$由$S$生成, 则$S$是平衡子欧拉符号图. 符号图$S$的线图$L(S)$也是一个符号图, 使得$L(S)$的点是$S$中的边, 其中$e_ie_j$是$L(S)$中的边当且仅当$e_i$和$e_j$在$S$中相邻,并且$e_ie_j$是$L(S)$中的负边当且仅当$e_i$和$e_j$在$S$中都是负边. 本文给出了两个符号图族$S$和$S''$,它们应用于刻画平衡子欧拉符号图和平衡子欧拉符号线图. 特别地, 本文证明了符号图$S$是平衡子欧拉的当且仅当$\not\in S$, $S$的符号线图是平衡子欧拉的当且仅当$S\not\in S''$.  相似文献   

13.
Denote by Q_m the generalized quaternion group of order 4m. Let R(Q_m) be its complex representation ring, and Δ(Q_m) its augmentation ideal. In this paper, the author gives an explicit Z-basis for the Δ~n(Q_m) and determines the isomorphism class of the n-th augmentation quotientΔ~n(Q_m)/(Δ~(n+1)(Q_m))for each positive integer n.  相似文献   

14.
Let S =∪(Gα : α ∈ E) be a semilattice of groups(i.e., a Cliford semigroup) and n a natural number. E is called an n-element chain of groups if it is an n-element chain. Denote by Cn the set of all n-element chains of groups. In this paper we shall show that for any natural number n, the class of semigroups Cn satisfies the strong isomorphism property.  相似文献   

15.
The moduli space of smooth curves admits a beautiful compactification $\mathcal{M}_{g,n} \subset \overline{\mathcal{M}}_{g,n}$ by the moduli space of stable curves. In this paper, we undertake a systematic classification of alternate modular compactifications of $\mathcal{M}_{g,n}$ . Let $\mathcal{U}_{g,n}$ be the (non-separated) moduli stack of all n-pointed reduced, connected, complete, one-dimensional schemes of arithmetic genus g. When g=0, $\mathcal{U}_{0,n}$ is irreducible and we classify all open proper substacks of $\mathcal{U}_{0,n}$ . When g≥1, $\mathcal{U}_{g,n}$ may not be irreducible, but there is a unique irreducible component $\mathcal{V}_{g,n} \subset\mathcal{U}_{g,n}$ containing $\mathcal{M}_{g,n}$ . We classify open proper substacks of $\mathcal {V}_{g,n}$ satisfying a certain stability condition.  相似文献   

16.
An nxn complex sign pattern(ray pattern) S is said to be spectrally arbitrary if for every monic nth degree polynomial f(λ) with coefficients from C,there is a complex matrix in the complex sign pattern class(ray pattern class) of S such that its characteristic polynomial is f(λ).We derive the Nilpotent-Centralizer methods for spectrally arbitrary complex sign patterns and ray patterns,respectively.We find that the Nilpotent-Centralizer methods for three kinds of patterns(sign pattern,complex sign pattern,ray pattern) are the same in form.  相似文献   

17.
To each irreducible infinite dimensional representation $(\pi ,\mathcal {H})$ of a C*‐algebra $\mathcal {A}$, we associate a collection of irreducible norm‐continuous unitary representations $\pi _{\lambda }^\mathcal {A}$ of its unitary group ${\rm U}(\mathcal {A})$, whose equivalence classes are parameterized by highest weights in the same way as the irreducible bounded unitary representations of the group ${\rm U}_\infty (\mathcal {H}) = {\rm U}(\mathcal {H}) \cap (\mathbf {1} + K(\mathcal {H}))$ are. These are precisely the representations arising in the decomposition of the tensor products $\mathcal {H}^{\otimes n} \otimes (\mathcal {H}^*)^{\otimes m}$ under ${\rm U}(\mathcal {A})$. We show that these representations can be realized by sections of holomorphic line bundles over homogeneous Kähler manifolds on which ${\rm U}(\mathcal {A})$ acts transitively and that the corresponding norm‐closed momentum sets $I_{\pi _\lambda ^\mathcal {A}}^{\bf n} \subseteq {\mathfrak u}(\mathcal {A})^{\prime }$ distinguish inequivalent representations of this type.  相似文献   

18.
Let $G$ be a finite group and $\mathfrak{c}(G)$ denote the number of cyclic subgroups of $G$. It is known that the minimal value of $\mathfrak{c}$ on the set of groups of order $n$, where $n$ is a positive integer, will occur at the cyclic group $Z_n$. In this paper, for non-cyclic nilpotent groups $G$ of order $n$, the lower bounds of $\mathfrak{c}(G)$ are established.  相似文献   

19.
Hay and, then, Johnson extended the classic Rice and Rice‐Shapiro Theorems for computably enumerable sets, to analogs for all the higher levels in the finite Ershov Hierarchy. The present paper extends their work (with some motivations presented) to analogs in the transfinite Ershov Hierarchy. Some of the transfinite cases are done for all transfinite notations in Kleene's important system of notations, $\mathcal {O}$. Other cases are done for all transfinite notations in a very natural, proper subsystem $\mathcal {O}_{\mathrm{Cantor}}$ of $\mathcal {O}$, where $\mathcal {O}_{\mathrm{Cantor}}$ has at least one notation for each constructive ordinal. In these latter cases it is open as to what happens for the entire set of transfinite notations in $(\mathcal {O} -\mathcal {O}_{\mathrm{Cantor}})$.  相似文献   

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