Non-trivial t-intersecting families for symplectic polar spaces
نویسندگان
چکیده
Let P be a symplectic polar space over finite field Fq, and Pm denote the set of all m-dimensional subspaces in P. We say t-intersecting subfamily is trivial if there exists t-dimensional subspace contained each member this family. In paper, we determine structure maximum sized non-trivial subfamilies Pm.
منابع مشابه
Weighted Non-Trivial Multiply Intersecting Families
Let n,r and t be positive integers. A family F of subsets of [n]={1,2, . . . ,n} is called r-wise t-intersecting if |F1∩·· ·∩Fr|≥ t holds for all F1, . . . ,Fr ∈F . An r-wise 1-intersecting family is also called an r-wise intersecting family for short. An r-wise t-intersecting family F is called non-trivial if |⋂F∈F F |<t. Let us define the Brace–Daykin structure as follows. F BD = {F ⊂ [n] : |...
متن کاملNon-trivial intersecting uniform sub-families of hereditary families
For a family F of sets, let μ(F) denote the size of a smallest set in F that is not a subset of any other set in F , and for any positive integer r, let F (r) denote the family of r-element sets in F . We say that a family A is of Hilton-Milner (HM ) type if for some A ∈ A, all sets in A\{A} have a common element x / ∈ A and intersect A. We show that if a hereditary family H is compressed and μ...
متن کاملIntersecting families of discrete structures are typically trivial
The study of intersecting structures is central to extremal combinatorics. A family of permutations F ⊂ Sn is t-intersecting if any two permutations in F agree on some t indices, and is trivial if all permutations in F agree on the same t indices. A k-uniform hypergraph is tintersecting if any two of its edges have t vertices in common, and trivial if all its edges share the same t vertices. Th...
متن کاملThe Intersection Structure of t-Intersecting Families
A family of sets is t-intersecting if any two sets from the family contain at least t common elements. Given a t-intersecting family of r-sets from an n-set, how many distinct sets of size k can occur as pairwise intersections of its members? We prove an asymptotic upper bound on this number that can always be achieved. This result can be seen as a generalization of the Erdős-Ko-Rado theorem.
متن کاملOn cross t-intersecting families of sets
For all p, t with 0 < p < 0.11 and 1≤ t ≤ 1/(2p), there exists n0 such that for all n,k with n > n0 and k/n = p the following holds: if A and B are k-uniform families on n vertices, and |A∩B| ≥ t holds for all A ∈A and B ∈B, then |A ||B| ≤ (n−t k−t )2 .
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2022
ISSN: ['1090-2465', '1071-5797']
DOI: https://doi.org/10.1016/j.ffa.2021.101955