共查询到20条相似文献,搜索用时 15 毫秒
1.
2.
The Number of Edge Colorings with no Monochromatic Cliques 总被引:1,自引:0,他引:1
Alon Noga; Balogh Jozsef; Keevash Peter; Sudakov Benny 《Journal London Mathematical Society》2004,70(2):273-288
Let F(n,r,k) denote the maximum possible number of distinctedge-colorings of a simple graph on n vertices with r colorswhich contain no monochromatic copy of Kk. It is shown thatfor every fixed k and all n>n0(k), and , where tk1(n)is the maximum possible number of edges of a graph on n verticeswith no Kk (determined by Turán's theorem). The caser=2 settles an old conjecture of Erds and Rothschild, whichwas also independently raised later by Yuster. On the otherhand, for every fixed r>3 and k>2, the function F(n,r,k)is exponentially bigger than . The proofs are based on Szemerédi's regularity lemmatogether with some additional tools in extremal graph theory,and provide one of the rare examples of a precise result provedby applying this lemma. 相似文献
3.
4.
5.
6.
7.
It is known that a strongly regular semi-Cayley graph (with respect to a group G) corresponds to a triple of subsets (C, D, D) of G. Such a triple (C, D, D) is called a partial difference triple. First, we study the case when D D is contained in a proper normal subgroup of G. We basically determine all possible partial difference triples in this case. In fact, when
nor 25, all partial difference triples come from a certain family of partial difference triples. Second, we investigate partial difference triples over cyclic group. We find a few nontrivial examples of strongly regular semi-Cayley graphs when |G| is even. This gives a negative answer to a problem raised by de Resmini and Jungnickel. Furthermore, we determine all possible parameters when G is cyclic. Last, as an application of the theory of partial difference triples, we prove some results concerned with strongly regular Cayley graphs. 相似文献
8.
9.
Tiberiu Constantinescu Aurelian Gheondea 《Proceedings of the American Mathematical Society》2000,128(9):2705-2713
In this paper we analyze the existence of a Schur algorithm and obtain coefficient characterizations for the functions in a generalized Schur class. An application to an interpolation problem of Carathéodory type raised by M.G. Krein and H. Langer is indicated.
10.
The k-tuple conjecture of Hardy and Little wood predicts that there are infinitely many primes p such that p+2 and p+6 are primes simultaneously.In this paper,we prove that there are infinitely many primes p such that Ω(p+2)≤3 and Ω(p+6)≤6,where Ω(n) denotes the total number of prime divisors of an integer n.We also prove a better conditional result,with the above Ω(p+6)≤6 replaced by Ω(p+6)≤3,under the Elliott-Halberstam conjecture. 相似文献
12.
Alexei Borodin 《Advances in Mathematics》2011,228(4):201
We construct discrete time Markov chains that preserve the class of Schur processes on partitions and signatures.One application is a simple exact sampling algorithm for qvolume-distributed skew plane partitions with an arbitrary back wall. Another application is a construction of Markov chains on infinite Gelfand–Tsetlin schemes that represent deterministic flows on the space of extreme characters of the infinite-dimensional unitary group. 相似文献
13.
u: A→H(I), I ε J], and let x: Q→S be the equalizer of ηS and Sη. 相似文献
14.
15.
16.
Let G = G(Φ, K) be a Chevalley group over a field K of characteristic ≠ 2. In the present paper, we classify the subgroups
of G generated by triples of long root subgroups, two of which are opposite, up to conjugacy. For finite fields, this result
is contained in papers by B. Cooperstein on the geometry of root subgroups, whereas for SL (n, K) it is proved in a paper by L. Di Martino and the first-named author. All interesting items of our list appear in deep
geometric results on abstract root subgroups and quadratic actions by F. Timmesfeld and A. Steinbach, and also by E. Bashkirov.
However, for applications to the groups of type E
l, we need a detailed justification of this list, which we could not extract from the published papers. That is why in the
present paper, we produce a direct elementary proof based on the reduction to D
4, where the question is settled by straightforward matrix calculations. Bibliography: 73 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 343, 2007, pp. 54–83. 相似文献
17.
G. W. Peck 《Studies in Applied Mathematics》1980,63(3):275-278
A construction is given for ordering triples chosen from an ordered set of elements, so that each triple agrees with each neighbor in two of its members and has third member that is a neighbor of its neighbor's third member. Neighbors here are adjacent in order, and also the first is neighbor to the last among both elements and triples. Joichi and White have given a different construction. 相似文献
18.
Stephanie van Willigenburg 《Annals of Combinatorics》2005,9(3):355-362
We determine the precise conditions under which any skew Schur function is equal to a Schur function over both infinitely
and finitely many variables.
Received May 29, 2004 相似文献
19.
The double Schur function is a natural generalization of the factorial Schur function introduced by Biedenharn and Louck. It also arises as the symmetric double Schubert polynomial corresponding to a class of permutations called Grassmannian permutations introduced by A. Lascoux. We present a lattice path interpretation of the double Schur function based on a flagged determinantal definition, which readily leads to a tableau interpretation similar to the original tableau definition of the factorial Schur function. The main result of this paper is a combinatorial treatment of the flagged double Schur function in terms of the lattice path interpretations of divided difference operators. Finally, we find lattice path representations of formulas for the symplectic and orthogonal characters for sp(2n) and so(2n + 1) based on the tableau representations due to King and El-Shakaway, and Sundaram. Based on the lattice path interpretations, we obtain flagged determinantal formulas for these characters. 相似文献
20.
In this paper we classify all Schur functions and skew Schur functions that are multiplicity free when expanded in the basis of fundamental quasisymmetric functions, termed F-multiplicity free. Combinatorially, this is equivalent to classifying all skew shapes whose standard Young tableaux have distinct descent sets. We then generalize our setting, and classify all F-multiplicity free quasisymmetric Schur functions with one or two terms in the expansion, or one or two parts in the indexing composition. This identifies composition shapes such that all standard composition tableaux of that shape have distinct descent sets. We conclude by providing such a classification for quasisymmetric Schur function families, giving a classification of Schur functions that are in some sense almost F-multiplicity free. 相似文献