The Turan number of a k-uniform hypergraph H,denoted by exk(n;H),is the maximum number of edges in any k-uniform hypergraph F on n vertices which does not contain H as a subgraph.Let Cl(k)denote the family of all k-un...The Turan number of a k-uniform hypergraph H,denoted by exk(n;H),is the maximum number of edges in any k-uniform hypergraph F on n vertices which does not contain H as a subgraph.Let Cl(k)denote the family of all k-uniform minimal cycles of length l;S(l1,…,lr)denote the family of hypergraphs consisting of unions of r vertex disjoint minimal cycles of lengthl1,…lr,respectively,and Cl(k)denote a k-uniform linear cycle of length l.We determine precisely exk(n;S(l1,…,lr)and exk(n;Cl1(k),…,Cl1(k)for sufficiently large n.Our results extend recent results of Füredi and Jiang who determined the Turan numbers for single k-uniform minimal cycles and linear cycles.展开更多
For A Zm and n ∈ Zm, let σA（n） be the number of solutions of equation n =x ＋ y, x, y ∈ A. Given a positive integer m, let Rm be the least positive integer r such that there exists a set A Zm with A ＋ A = Zm ...For A Zm and n ∈ Zm, let σA（n） be the number of solutions of equation n =x ＋ y, x, y ∈ A. Given a positive integer m, let Rm be the least positive integer r such that there exists a set A Zm with A ＋ A = Zm and σA（n） ≤ r. Recently, Chen Yonggao proved that all Rm ≤ 288. In this paper, we obtain new upper bounds of some special type Rkp2.展开更多
Ying Guang Shi(1995 & 1999) obtained some quadratures, which is based onthe zeros of the so-called s-orthogonal polynomials with respect to some JacobiB.Bojanov(1996) and our recent work, we give here a simple and...Ying Guang Shi(1995 & 1999) obtained some quadratures, which is based onthe zeros of the so-called s-orthogonal polynomials with respect to some JacobiB.Bojanov(1996) and our recent work, we give here a simple and unified approachto these questions of this type and obtain quadratures in terms of the divided differ-ences, which is based on an appropriate representation of the Hermite interpolatingpolynomial, of corresponding function at the zeros of the appropriate s-orthogonalpolynomial with multiplicities.展开更多
基金partially supported by the National Natural Science Foundation of China(Nos.12131013,11871034)partially supported by the National Natural Science Foundation of China(Nos.11922112,12161141006)the Natural Science Foundation of Tianjin(Nos.20JCZDJC00840,20JCJQJC00090)。
文摘The Turan number of a k-uniform hypergraph H,denoted by exk(n;H),is the maximum number of edges in any k-uniform hypergraph F on n vertices which does not contain H as a subgraph.Let Cl(k)denote the family of all k-uniform minimal cycles of length l;S(l1,…,lr)denote the family of hypergraphs consisting of unions of r vertex disjoint minimal cycles of lengthl1,…lr,respectively,and Cl(k)denote a k-uniform linear cycle of length l.We determine precisely exk(n;S(l1,…,lr)and exk(n;Cl1(k),…,Cl1(k)for sufficiently large n.Our results extend recent results of Füredi and Jiang who determined the Turan numbers for single k-uniform minimal cycles and linear cycles.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 10901002 10771103)
文摘For A Zm and n ∈ Zm, let σA（n） be the number of solutions of equation n =x ＋ y, x, y ∈ A. Given a positive integer m, let Rm be the least positive integer r such that there exists a set A Zm with A ＋ A = Zm and σA（n） ≤ r. Recently, Chen Yonggao proved that all Rm ≤ 288. In this paper, we obtain new upper bounds of some special type Rkp2.
文摘Ying Guang Shi(1995 & 1999) obtained some quadratures, which is based onthe zeros of the so-called s-orthogonal polynomials with respect to some JacobiB.Bojanov(1996) and our recent work, we give here a simple and unified approachto these questions of this type and obtain quadratures in terms of the divided differ-ences, which is based on an appropriate representation of the Hermite interpolatingpolynomial, of corresponding function at the zeros of the appropriate s-orthogonalpolynomial with multiplicities.
