共查询到20条相似文献,搜索用时 10 毫秒
1.
Luc Lapointe 《Advances in Mathematics》2007,213(1):183-204
We study k-Schur functions characterized by k-tableaux, proving combinatorial properties such as a k-Pieri rule and a k-conjugation. This new approach relies on developing the theory of k-tableaux, and includes the introduction of a weight-permuting involution on these tableaux that generalizes the Bender-Knuth involution. This work lays the groundwork needed to prove that the set of k-Schur Littlewood-Richardson coefficients contains the 3-point Gromov-Witten invariants; structure constants for the quantum cohomology ring. 相似文献
2.
Guangshi Lü 《Journal of Number Theory》2008,128(4):805-819
In this paper, we are able to sharpen Hua's classical result by showing that each sufficiently large integer can be written as
3.
It is a well-known result of Tutte that, for every element x of a connected matroid M, at least one of the deletion and contraction of x from M is connected. This paper shows that, in a connected k-polymatroid, only two such elements are guaranteed. We show that this bound is sharp and characterize those 2-polymatroids that achieve this minimum. To this end, we define and make use of a generalized parallel connection for k-polymatroids that allows connecting across elements of different ranks. This study of essential elements gives results crucial to finding the unavoidable minors of connected 2-polymatroids, which will appear elsewhere. 相似文献
4.
5.
We give several results about the asymptotic behaviour of matroids. Specifically, almost all matroids are simple and cosimple and, indeed, are 3-connected. This verifies a strengthening of a conjecture of Mayhew, Newman, Welsh, and Whittle. We prove several quantitative results including giving bounds on the rank, a bound on the number of bases, the number of circuits, and the maximum circuit size of almost all matroids. 相似文献
6.
Wenguang Zhai 《Journal of Number Theory》2009,129(8):1820-1836
For a fixed prime q, let eq(n) denote the order of q in the prime factorization of n!. For two fixed integers m?2 and r with 0?r?m−1, let A(x;m,q,r) denote the numbers of positive integers n?x for which . In this paper we shall prove a sharp asymptotic formula of A(x;m,q,r). 相似文献
7.
In this paper we deal with monogenic and k-hypermonogenic automorphic forms on arithmetic subgroups of the Ahlfors-Vahlen group. Monogenic automorphic forms are exactly the 0-hypermonogenic automorphic forms. In the first part we establish an explicit relation between k-hypermonogenic automorphic forms and Maaß wave forms. In particular, we show how one can construct from any arbitrary non-vanishing monogenic automorphic form a Clifford algebra valued Maaß wave form. In the second part of the paper we compute the Fourier expansion of the k-hypermonogenic Eisenstein series which provide us with the simplest non-vanishing examples of k-hypermonogenic automorphic forms. 相似文献
8.
We develop the Turán sieve and a ‘simple sieve’ in the context of bipartite graphs and apply them to various problems in combinatorics. More precisely, we provide applications in the cases of characters of abelian groups, vertex-colourings of graphs, Latin squares, connected graphs, and generators of groups. In addition, we give a spectral interpretation of the Turán sieve. 相似文献
9.
Zaizhao Meng 《Journal of Number Theory》2006,121(1):45-66
In this paper we obtain an improved asymptotic formula on the frequency of k-free numbers with a given difference. We also give a new upper bound of Barban-Davenport-Halberstam type for the k-free numbers in arithmetic progressions. 相似文献
10.
Hebing Rui 《Journal of Combinatorial Theory, Series A》2005,111(1):78-88
In this paper, we give a necessary and sufficient condition for a Brauer algebra to be semisimple. 相似文献
11.
Let p, q be primes and m be a positive integer. For a positive integer n, let ep(n) be the nonnegative integer with pep(n)|n and pep(n)+1?n. The following results are proved: (1) For any positive integer m, any prime p and any ε∈Zm, there are infinitely many positive integers n such that ; (2) For any positive integer m, there exists a constant D(m) such that if ε,δ∈Zm and p, q are two distinct primes with max{p,q}?D(m), then there exist infinitely many positive integers n such that , . Finally we pose four open problems. 相似文献
12.
13.
A weighted graph is one in which every edge e is assigned a nonnegative number w(e), called the weight of e. The weight of a cycle is defined as the sum of the weights of its edges. The weighted degree of a vertex is the sum of the weights of the edges incident with it. In this paper, we prove that: Let G be a k-connected weighted graph with k?2. Then G contains either a Hamilton cycle or a cycle of weight at least 2m/(k+1), if G satisfies the following conditions: (1) The weighted degree sum of any k+1 pairwise nonadjacent vertices is at least m; (2) In each induced claw and each induced modified claw of G, all edges have the same weight. This generalizes an early result of Enomoto et al. on the existence of heavy cycles in k-connected weighted graphs. 相似文献
14.
Yingchun Cai 《Journal of Number Theory》2008,128(5):1336-1357
Let N be a sufficiently large even integer and S(N) denote the number of solutions of the equation
N=p+P2, 相似文献
15.
William D. Banks 《Journal of Number Theory》2006,120(2):326-348
We establish an asymptotic formula for the number of positive integers n?x for which φ(n) is free of kth powers. 相似文献
16.
17.
We prove the estimate
for the number Ek(N)
of k-tuples
(n + a1,..., n + ak) of primes not exceeding N,
for k of size c1 log N and
N sufficiently large.
A bound of this strength was previously known in the special case
<
only, (Vaughan, 1973). For general ai this is an improvement upon the work of
Hofmann and Wolke (1996).
The number of prime tuples of this size has
considerable oscillations, when varying the prime pattern.
Received: 20 December 2002 相似文献
18.
Jiaojiao Wu 《Discrete Mathematics》2008,308(12):2637-2642
This paper discusses the game colouring number of partial k-trees and planar graphs. Let colg(PTk) and colg(P) denote the maximum game colouring number of partial k trees and the maximum game colouring number of planar graphs, respectively. In this paper, we prove that colg(PTk)=3k+2 and colg(P)?11. We also prove that the game colouring number colg(G) of a graph is a monotone parameter, i.e., if H is a subgraph of G, then colg(H)?colg(G). 相似文献
19.
Xianmeng Meng 《Journal of Number Theory》2009,129(10):2504-2518
Let Pk denote any integer with no more than k prime factors, counted according to multiplicity. It is proved that for every sufficiently large odd integer , the equation p1+p2+p3=n is solvable in prime variables p1,p2,p3 such that p1+2=P2, , and for almost all sufficiently large even integer , the equation p1+p2=n is solvable in prime variables p1,p2 such that p1+2=P2. 相似文献
20.
Yong-Gao Chen 《Journal of Number Theory》2003,98(2):310-319
In this paper we prove that if (r,12)?3, then the set of positive odd integers k such that kr−2n has at least two distinct prime factors for all positive integers n contains an infinite arithmetic progression. The same result corresponding to kr2n+1 is also true. 相似文献