Voting Fairly: Transitive Maximal Intersecting Families of Sets
نویسندگان
چکیده
منابع مشابه
Voting Fairly: Transitive Maximal Intersecting Families of Sets
There are several applications of maximal intersecting families (MIFs) and different notions of fairness. We survey known results regarding the enumeration of MIFs, and we conclude the enumeration of the 207,650,662,008 maximal families of intersecting subsets of X whose group of symmetries is transitive for |X |<13. 2000 Academic Press
متن کاملMaximal Intersecting Families of Finite Sets and «uniform Hjelmslev Planes
The following theorem is proved. The collection of lines of an n-uniform projective Hjelmslev plane is maximal when considered as a collectiion of mutually intersecting sets of equal cardinality.
متن کاملMultiply intersecting families of sets
Let [n] denote the set {1, 2, ..., n}, 2 the collection of all subsets of [n] and F ⊂ 2 be a family. The maximum of |F| is studied if any r subsets have an at least s-element intersection and there are no ` subsets containing t+1 common elements. We show that |F| ≤ Pt−s i=0 n−s i + t+`−s t+2−s n−s t+1−s + `− 2 and this bound is asymptotically the best possible as n →∞ and t ≥ 2s ≥ 2, r, ` ≥ 2 a...
متن کاملIntersecting Balanced Families of Sets
Suppose that any t members (t ≥ 2) of a regular family on an n element set have at least k common elements. It is proved that the largest member of the family has at least k1/tn1−1/t elements. The same holds for balanced families, which is a generalization of the regularity. The estimate is asymptotically sharp.
متن کاملAlmost Intersecting Families of Sets
Let us write DF (G) = {F ∈ F : F ∩ G = ∅} for a set G and a family F . Then a family F of sets is said to be (≤ l)-almost intersecting (l-almost intersecting) if for any F ∈ F we have |DF (F )| ≤ l (|DF (F )| = l). In this paper we investigate the problem of finding the maximum size of an (≤ l)almost intersecting (l-almost intersecting) family F . AMS Subject Classification: 05D05
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: Journal of Combinatorial Theory, Series A
سال: 2000
ISSN: 0097-3165
DOI: 10.1006/jcta.2000.3103