Author Keywords: Bounded in probability; convergence in probability; cotype; uniform tightness condition 相似文献
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1.
Xuding Zhu 《Discrete Mathematics》1998,190(1-3):215-222
Suppose G is a graph. The chromatic Ramsey number rc(G) of G is the least integer m such that there exists a graph F of chromatic number m for which the following is true: for any 2-colouring of the edges of F there is a monochromatic subgraph isomorphic to G. Let Mn = min[rc(G): χ(G) = n]. It was conjectured by Burr et al. (1976) that Mn = (n − 1)2 + 1. This conjecture has been confirmed previously for n 4. In this paper, we shall prove that the conjecture is true for n = 5. We shall also improve the upper bounds for M6 and M7. 相似文献
2.
Suppose A∈Mn×m(F), B∈Mn×t(F) for some field F. Define Г(AB) to be the set of n×n diagonal matrices D such that the column space of DA is contained in the column space of B. In this paper we determine dim Г(AB). For matrices AB of the same rank we provide an algorithm for computing dim Г(AB). 相似文献
3.
Maximal IM-unextendable graphs 总被引:3,自引:0,他引:3
A graph G is maximal IM-unextendable if G is not induced matching extendable and, for every two nonadjacent vertices x and y, G+xy is induced matching extendable. We show in this paper that a graph G is maximal IM-unextendable if and only if G is isomorphic to Mr(Ks(Kn1Kn2Knt)), where Mr is an induced matching of size r, r1, t=s+2, and each ni is odd. 相似文献
4.
Deng Pin Liu 《数学学报(英文版)》2018,34(11):1742-1754
Let Pn be a simple n-polytope with a Z2-characteristic function λ. And h is a Morse function over Pn. Then the small cover Mn(λ) corresponding to the pair (Pn, λ) has a cell structure given by h. From this cell structure we can derive a cellular chain complex of Mn(λ) with integer coefficients. In this paper, firstly, we discuss the highest dimensional boundary morphism ∂n of this cellular chain complex and get that ∂n=0 or 2 by a natural way. And then, from the well-known result that the submanifold corresponding to (F, λF) is naturally a small cover with dimension k, where F is any k-face of Pn and λF is the restriction of λ on F, we get that ∂k=0 or ±2 for 0 ≤ k < n. Finally, by using the definition of inherited characteristic function which is the restriction of λ on the faces of Pn, we get a way to calculate the homology groups of Mn(λ). Applying our result to a 3-small cover we have that the homology groups of any 3-small cover is torsion-free or has only 2-torsion. 相似文献
5.
A mapping ƒ : n=1∞In → I is called a bag mapping having the self-identity if for every (x1,…,xn) ε i=1∞In we have (1) ƒ(x1,…,xn) = ƒ(xi1,…,xin) for any arrangement (i1,…,in) of {1,…,n}; monotonic; (3) ƒ(x1,…,xn, ƒ(x1,…,xn)) = ƒ(x1,…,xn). Let {ωi,n : I = 1,…,n;n = 1,2,…} be a family of non-negative real numbers satisfying Σi=1nωi,n = 1 for every n. Then one calls the mapping ƒ : i=1∞In → I defined as follows an OWA bag mapping: for every (x1,…,xn) ε i=1∞In, ƒ(x1,…,xn) = Σi=1nωi,nyi, where yi is the it largest element in the set {x1,…,xn}. In this paper, we give a sufficient and necessary condition for an OWA bag mapping having the self-identity. 相似文献
6.
In this note, we show that the set of all commuting d-tuples of commuting n×n matrices that are contained in an n-dimensional commutative algebra is a closed set, and therefore, Gerstenhaber's theorem on commuting pairs of matrices is a consequence of the irreduciblity of the variety of commuting pairs. We show that the variety of commuting triples of 4×4 matrices is irreducible. We also study the variety of n-dimensional commutative subalgebras of Mn(F), and show that it is irreducible of dimension n2−n for n4, but reducible, of dimension greater than n2−n for n7. 相似文献
7.
《Discrete Mathematics》1999,200(1-3):137-147
We form squares from the product of integers in a short interval [n, n + tn], where we include n in the product. If p is prime, p|n, and (2p) > n, we prove that p is the minimum tn. If no such prime exists, we prove tn √5n when n> 32. If n = p(2p − 1) and both p and 2p − 1 are primes, then tn = 3p> 3 √n/2. For n(n + u) a square > n2, we conjecture that a and b exist where n < a < b < n + u and nab is a square (except n = 8 and N = 392). Let g2(n) be minimal such that a square can be formed as the product of distinct integers from [n, g2(n)] so that no pair of consecutive integers is omitted. We prove that g2(n) 3n − 3, and list or conjecture the values of g2(n) for all n. We describe the generalization to kth powers and conjecture the values for large n. 相似文献
8.
In this paper, we investigate the asymptotic behaviors of the critical branching process with immigration {Z_n, n ≥ 0}. First we get some estimation for the probability generating function of Zn. Based on it, we get a large deviation for Z_(n+1)/Z_n. Lower and upper deviations for Zn are also studied. As a by-product, an upper deviation for max_(1≤i≤n) Z_i is obtained. 相似文献
9.
The Ramsey number r(H,Kn) is the smallest integer N so that each graph on N vertices that fails to contain H as a subgraph has independence number at least n. It is shown that r(K2,m,Kn)(m−1+o(1))(n/log n)2 and r(C2m,Kn)c(n/log n)m/(m−1) for m fixed and n→∞. Also r(K2,n,Kn)=Θ(n3/log2 n) and
. 相似文献
10.
Shannon L. Fitzpatrick Richard J. Nowakowski Derek Holton Ian Caines 《Discrete Mathematics》2001,240(1-3):253-260
An isometric path is merely any shortest path between two vertices. If the vertices of the hypercube Qn are represented by the set of 0–1 vectors of length n, an isometric path is obtained by changing the coordinates of a vector one at a time, never changing the same coordinate more than once. The minimum number of isometric paths required to cover the vertices of Qn is at least 2n/(n+1). We show that when n+1 is a power of 2, the lower bound is in fact the minimum. In doing so, we construct a family of disjoint isometric paths which can be used to find an upper bound for additional classes of hypercubes. 相似文献
11.
Let C be a planar region. Choose n points p1,,pnI.I.D. from the uniform distribution over C. Let MCn be the number of these points that are maximal. If C is convex it is known that either E(MCn)=Θ(√n)> or E(MCn)=O(log n). In this paper we will show that, for general C, there is very little that can be said, a-priori, about E(MCn). More specifically we will show that if g is a member of a large class of functions then there is always a region C such that E(MCn)=Θ(g(n)). This class contains, for example, all monotically increasing functions of the form g(n)= nlnβn, where 0<<1 and β0. This class also contains nondecreasing functions like g(n)=ln*n. The results in this paper remain valid in higher dimensions. 相似文献
12.
Gwang-Yeon Lee 《Linear algebra and its applications》2000,320(1-3):51-61
For a positive integer k2, the k-Fibonacci sequence {gn(k)} is defined as: g1(k)==gk−2(k)=0, gk−1(k)=gk(k)=1 and for n>k2, gn(k)=gn−1(k)+gn−2(k)++gn−k(k). Moreover, the k-Lucas sequence {ln(k)} is defined as ln(k)=gn−1(k)+gn+k−1(k) for n1. In this paper, we consider the relationship between gn(k) and ln(k) and 1-factors of a bipartite graph. 相似文献
13.
H. P. Yap 《Discrete Mathematics》1995,140(1-3):245-252
We generalize two results of Hilton on total-colourings of a graph. The first generalized result unifies several previous results/proof techniques of Bermond, Chen, Chew, Fu, Hilton, Wang, and Yap. Applying the second generalized result, we prove that if G Kn, n is such that Δ(G) = n − 1 and the complement of G with respect to Kn, n contains a 1-factor, then its total chromatic number is Δ(G) + 1. 相似文献
14.
Bipartite dimensions and bipartite degrees of graphs 总被引:2,自引:0,他引:2
A cover (bipartite) of a graph G is a family of complete bipartite subgraphs of G whose edges cover G's edges. G'sbipartite dimension d(G) is the minimum cardinality of a cover, and its bipartite degree η(G) is the minimum over all covers of the maximum number of covering members incident to a vertex. We prove that d(G) equals the Boolean interval dimension of the irreflexive complement of G, identify the 21 minimal forbidden induced subgraphs for d 2, and investigate the forbidden graphs for d n that have the fewest vertices. We note that for complete graphs, d(Kn) = [log2n], η(Kn) = d(Kn) for n 16, and η(Kn) is unbounded. The list of minimal forbidden induced subgraphs for η 2 is infinite. We identify two infinite families in this list along with all members that have fewer than seven vertices. 相似文献
15.
Let Dn(r) denote the convex hull of degree sequences of simple r-uniform hypergraphs on the vertex set {1,2,…,n}. The polytope Dn(2) is a well-studied object. Its extreme points are the threshold sequences (i.e., degree sequences of threshold graphs) and its facets are given by the Erdös–Gallai inequalities. In this paper we study the polytopes Dn(r) and obtain some partial information. Our approach also yields new, simple proofs of some basic results on Dn(2). Our main results concern the extreme points and facets of Dn(r). We characterize adjacency of extreme points of Dn(r) and, in the case r=2, determine the distance between two given vertices in the graph of Dn(2). We give a characterization of when a linear inequality determines a facet of Dn(r) and use it to bound the sizes of the coefficients appearing in the facet defining inequalities; give a new short proof for the facets of Dn(2); find an explicit family of Erdös–Gallai type facets of Dn(r); and describe a simple lifting procedure that produces a facet of Dn+1(r) from one of Dn(r). 相似文献
16.
Norbert Henze 《Statistics & probability letters》1998,40(4):321-327
In number lotteries people choose r numbers out of s. Weekly published “drawings since hit tables” indicate how many drawings have taken place since each of the s numbers was last selected as a winning number. Among many lotto players, they enhance the widespread belief that numbers should be “due” if they have not come up for a long time. Under the assumptions of independence of the drawings and equiprobability of all possible combinations, the random s-vectors Yn, n 1, of entries in a drawings since hit table after n drawings form a Markov chain. The limit distribution of Yn as n → ∞ is a new multivariate generalization of the geometric distribution. The determination of the distribution of the maximum entry in a drawings since hit table within the first n draws of a lottery seems to be an open problem. 相似文献
17.
Let X be the vertex set of KnA k-cycle packing of Kn is a triple (X,C,L), where C is a collection of edge disjoint k-cycles of Kn and L is the collection of edges of Kn not belonging to any of the k-cycles in C. A k-cycle packing (X,C,L) is called resolvable if C can be partitioned into almost parallel classes. A resolvable maximum k-cycle packing of Kn, denoted by k-RMCP(n), is a resolvable k-cycle packing of Kn, (X,C,L), in which the number of almost parallel classes is as large as possible. Let D(n, k) denote the number of almost parallel classes in a k-RMCP(n). D(n, k) for k = 3, 4 has been decided. When n ≡ k (mod 2k) and k ≡ 1 (mod 2) or n ≡ 1 (mod 2k) and k ∈{6, 8, 10, 14}∪{m: 5≤m≤49, m ≡ 1 (mod 2)}, D(n, k) also has been decided with few possible exceptions. In this paper, we shall decide D(n, 5) for all values of n≥5. 相似文献
18.
Asymptotic behavior of a nonlinear delay difference equation 总被引:1,自引:0,他引:1
J. YanB. Liu 《Applied Mathematics Letters》1995,8(6):1-5
This paper considers a class of nonlinear difference equations . A necessary and sufficient condition for the existence of a bounded nonoscillatory solution is given. 相似文献
Δ3yn + ƒ(n, yn, yn−r) = 0, n N (n0)
19.
Let Mbe a monoid. A ring Ris called M-π-Armendariz if whenever α = a1g1+ a2g2+ · · · + angn, β = b1h1+ b2h2+ · · · + bmhm ∈ R[M] satisfy αβ ∈ nil(R[M]), then aibj ∈ nil(R) for all i, j. A ring R is called weakly 2-primal if the set of nilpotent elements in R coincides with its Levitzki radical. In this paper, we consider some extensions of M-π-Armendariz rings and further investigate their properties under the condition that R is weakly 2-primal. We prove that if R is an M-π-Armendariz ring then nil(R[M]) = nil(R)[M]. Moreover, we study the relationship between the weak zip-property (resp., weak APP-property, nilpotent p.p.-property, weak associated prime property) of a ring R and that of the monoid ring R[M] in case R is M-π-Armendariz. 相似文献
20.
Xiang Chen Wang 《Statistics & probability letters》1990,10(5):391-396
Let B be a separable Banach space. The following is one of the results proved in this paper. The Banach space B is of cotype p if and only if
1. dn, n 1, has no subsequence converging in probability, and
2. ∑n 1|an|p < ∞ whenever ∑n 1andn converges almost surely are equivalent for every sequence dn, n 1, of symmetric independent random elements taking values in B.