منابع مشابه
Counting of Moore Families for n=7
Given a set Un = {0, 1, ..., n−1}, a collectionM of subsets of Un that is closed under intersection and contains Un is known as a Moore family. The set of Moore families for a given n, denoted by Mn, increases very quickly with n, thus |M3| is 61 and |M4| is 2480. In [1] the authors determined the number for n = 6 and stated a 24hcomputation-time. Thus, the number for n = 7 can be considered as...
متن کاملPoint Counting in Families of Hyperelliptic Curves
Let EΓ be a family of hyperelliptic curves defined by Y 2 = Q(X,Γ), where Q is defined over a small finite field of odd characteristic. Then with γ in an extension degree n field over this small field, we present a deterministic algorithm for computing the zeta function of the curve Eγ by using Dwork deformation in rigid cohomology. The complexity of the algorithm is O(n) and it needs O(n) bits...
متن کاملSome hard families of parameterised counting problems
We consider parameterised subgraph-counting problems of the following form: given a graph G, how many k-tuples of its vertices have a given property? A number of such problems are known to be #W[1]complete; here we substantially generalise some of these existing results by proving hardness for two large families of such problems. We demonstrate that it is #W[1]-hard to count the number of k-ver...
متن کاملCounting Families of Mutually Intersecting Sets
We determine the number of maximal intersecting families on a 9-set and find 423295099074735261880. We determine the number of independent sets of the Kneser graph K(9, 4) and find 366996244568643864340. Finally, we determine the number of intersecting families on an 8-set and find 14704022144627161780744368338695925293142507520.
متن کاملCounting Intersecting and Pairs of Cross-Intersecting Families
A family of subsets of {1, . . . , n} is called intersecting if any two of its sets intersect. A classical result in extremal combinatorics due to Erdős, Ko, and Rado determines the maximum size of an intersecting family of k-subsets of {1, . . . , n}. In this paper we study the following problem: how many intersecting families of k-subsets of {1, . . . , n} are there? Improving a result of Bal...
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ژورنال
عنوان ژورنال: Sociology Compass
سال: 2015
ISSN: 1751-9020
DOI: 10.1111/soc4.12273