constant whenever （x, y）∈Rk. This constant is denoted by p<sub>ij</sub><sup>k</sup>. Then we call X=(X,{Ri}<sub>0≤i≤d</sub>) and association scheme of class d on X. The non-neg...constant whenever （x, y）∈Rk. This constant is denoted by p<sub>ij</sub><sup>k</sup>. Then we call X=(X,{Ri}<sub>0≤i≤d</sub>) and association scheme of class d on X. The non-negative integers p<sub>ij</sub><sup>k</sup> are called the intersection numbers of X.展开更多
In this paper, we investigate the intersection numbers of nearly Kirkman triple systems.JN[V] is the set of all integers k such that there is a pair of NKTS（v）s with a common uncovered collection of 2-subset interse...In this paper, we investigate the intersection numbers of nearly Kirkman triple systems.JN[V] is the set of all integers k such that there is a pair of NKTS（v）s with a common uncovered collection of 2-subset intersecting in k triples. It has been established that JN[v] = {0, 1,. v（v-2）/6-6,v（v-2）/6-4,v（v-2）/6} for any integers v = 0 （mod 6） and v ≥ 66. For v ≤ 60, there are 8 cases leftundecided.展开更多
The intersection number, in (G), has been defined as the minimumcardinality of a set S which has n different subsets S_i such that each S_i can beassigned to the node v_i of G and nodes v_i, v_j are adjacent if and on...The intersection number, in (G), has been defined as the minimumcardinality of a set S which has n different subsets S_i such that each S_i can beassigned to the node v_i of G and nodes v_i, v_j are adjacent if and onlyif S_i∩S_j ≠0. We introduce the multiset intersection number min (G), defined similarly exceptthat multisets with elements in S may now be assigned to the nodes of G. Weprove that min (G) equals the smallest number ofcliques of G whose union is G.展开更多
We compute some tautological bundles on Hilbert the intersection numbers of two generating series of integrals related to schemes of points on surfaces SIn], including Chern classes of tautological bundles, and the E...We compute some tautological bundles on Hilbert the intersection numbers of two generating series of integrals related to schemes of points on surfaces SIn], including Chern classes of tautological bundles, and the Euler characteristics of Α_yTS[n]. We also propose some related conjectures, including an equivariant version of Lehn＇s conjecture.展开更多
The problem of embedding spheres in rational surfaces CP 2#n $\overline {CP} $ 2 is studied. For homology classes u = (b 1 + k, b 2,...,b n) with positive self-intersection numbers, a necessary and sufficient conditio...The problem of embedding spheres in rational surfaces CP 2#n $\overline {CP} $ 2 is studied. For homology classes u = (b 1 + k, b 2,...,b n) with positive self-intersection numbers, a necessary and sufficient condition to detect its representability is given when k ≤ 5.展开更多
Ever since the famous Erd os-Ko-Rado theorem initiated the study of intersecting families of subsets,extremal problems regarding intersecting properties of families of various combinatorial objects have been extensive...Ever since the famous Erd os-Ko-Rado theorem initiated the study of intersecting families of subsets,extremal problems regarding intersecting properties of families of various combinatorial objects have been extensively investigated.Among them,studies about families of subsets,vector spaces and permutations are of particular concerns.Recently,we proposed a new quantitative intersection problem for families of subsets:For F([n]k),define its total intersection number as I(F)=ΣF1;F2∈F|F1∩F2|.Then,what is the structure of F when it has the maximal total intersection number among all the families in([n]k)with the same family size?In a recent paper,Kong and Ge(2020)studied this problem and characterized extremal structures of families maximizing the total intersection number of given sizes.In this paper,we consider the analogues of this problem for families of vector spaces and permutations.For certain ranges of family sizes,we provide structural characterizations for both families of subspaces and families of permutations having maximal total intersection numbers.To some extent,these results determine the unique structure of the optimal family for some certain values of jFj and characterize the relationship between having the maximal total intersection number and being intersecting.Besides,we also show several upper bounds on the total intersection numbers for both families of subspaces and families of permutations of given sizes.展开更多
文摘constant whenever （x, y）∈Rk. This constant is denoted by p<sub>ij</sub><sup>k</sup>. Then we call X=(X,{Ri}<sub>0≤i≤d</sub>) and association scheme of class d on X. The non-negative integers p<sub>ij</sub><sup>k</sup> are called the intersection numbers of X.
基金Supported by the Fundamental Research Funds for the Central Universities(Grant No.2014JBM121)National Natural Science Foundation of China(Grant Nos.11271042,11471032 and 11571034)
文摘In this paper, we investigate the intersection numbers of nearly Kirkman triple systems.JN[V] is the set of all integers k such that there is a pair of NKTS（v）s with a common uncovered collection of 2-subset intersecting in k triples. It has been established that JN[v] = {0, 1,. v（v-2）/6-6,v（v-2）/6-4,v（v-2）/6} for any integers v = 0 （mod 6） and v ≥ 66. For v ≤ 60, there are 8 cases leftundecided.
文摘The intersection number, in (G), has been defined as the minimumcardinality of a set S which has n different subsets S_i such that each S_i can beassigned to the node v_i of G and nodes v_i, v_j are adjacent if and onlyif S_i∩S_j ≠0. We introduce the multiset intersection number min (G), defined similarly exceptthat multisets with elements in S may now be assigned to the nodes of G. Weprove that min (G) equals the smallest number ofcliques of G whose union is G.
基金The second author was partially supported by the National Natural Science Foundation of China （Grant No. 11171174）.
文摘We compute some tautological bundles on Hilbert the intersection numbers of two generating series of integrals related to schemes of points on surfaces SIn], including Chern classes of tautological bundles, and the Euler characteristics of Α_yTS[n]. We also propose some related conjectures, including an equivariant version of Lehn＇s conjecture.
文摘The problem of embedding spheres in rational surfaces CP 2#n $\overline {CP} $ 2 is studied. For homology classes u = (b 1 + k, b 2,...,b n) with positive self-intersection numbers, a necessary and sufficient condition to detect its representability is given when k ≤ 5.
基金supported by National Natural Science Foundation of China (Grant No. 11971325)National Key Research and Development Program of China (Grant Nos. 2020YFA0712100 and 2018YFA0704703)Beijing Scholars Program
文摘Ever since the famous Erd os-Ko-Rado theorem initiated the study of intersecting families of subsets,extremal problems regarding intersecting properties of families of various combinatorial objects have been extensively investigated.Among them,studies about families of subsets,vector spaces and permutations are of particular concerns.Recently,we proposed a new quantitative intersection problem for families of subsets:For F([n]k),define its total intersection number as I(F)=ΣF1;F2∈F|F1∩F2|.Then,what is the structure of F when it has the maximal total intersection number among all the families in([n]k)with the same family size?In a recent paper,Kong and Ge(2020)studied this problem and characterized extremal structures of families maximizing the total intersection number of given sizes.In this paper,we consider the analogues of this problem for families of vector spaces and permutations.For certain ranges of family sizes,we provide structural characterizations for both families of subspaces and families of permutations having maximal total intersection numbers.To some extent,these results determine the unique structure of the optimal family for some certain values of jFj and characterize the relationship between having the maximal total intersection number and being intersecting.Besides,we also show several upper bounds on the total intersection numbers for both families of subspaces and families of permutations of given sizes.
