1篇
您的检索式：作者名="Yuanxiao Xi"
|
|
|
题名
|
作者
|
年代
|
出处
|
被引量
|
| 1 | Inverse problems of the Erdos-Ko-Rado type theorems for families of vector spaces and permutations显示文摘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. | Xiangliang Kong Yuanxiao Xi Bingchen Qian Gennian Ge | 2022 | Science China Mathematics2022，65，5： | 0 |
您所在的机构暂未开通此部分的功能，请联系管理员