Given 3n points in the unit square, n >12, they determine n triangles whose vertices exhaust the given 3n points in many ways. Choose the n triangles so that the sum of their areas is minimal, and let a\*(n) be the maximum value of this minimum over all configurations of 3n points. Then n-~<< a\*(n)
Partitioning sets of quadruples into designs I
β Scribed by Martin J. Sharry; Anne Penfold Street
- Publisher
- Elsevier Science
- Year
- 1989
- Tongue
- English
- Weight
- 460 KB
- Volume
- 77
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
All of the non-isomorphic ways of partitioning the collection of all the quadruples chosen from a set of eight elements into five disjoint 2- (8,4,3) designs are determined.
π SIMILAR VOLUMES
It is shown in this note that it can be recognized in polynomial time whether the vertex set of a finite undirected graph can be partitioned into one or two independent sets and one or two cliques. Such graphs generalize bipartite and split graphs and the result also shows that it can be recognized
For I G t < k CI u. let S(t, k, u) denote a Steiner system and let Pr, (u) be the set of all k-subsets of theset {i,2,..., u}. We partition PJ 13) into 55 mutually disjoint S(2.4, 13)'s (projective planes). This is the first known example of a complete partition of Pk(u) into disjoint S(t, k, u)'s f
A partition u of [k] = {1, 2, . . . , k} is contained in another partition v of [l] if [l] has a k-subset on which v induces u. We are interested in counting partitions v not containing a given partition u or a given set of partitions R. This concept is related to that of forbidden permutations. A s
Tverberg's 1966 theorem asserts that every set X of (m -1)(d + 1) + 1 points in R d has a partition X 1 , X 2 , . . . , X m such that m i=1 conv X i = Ο. We give a short and elementary proof of a theorem on convex cones which generalizes this result. As a consequence, we deduce several divisibility
The physical arrangement of an active noise control system (control sources and error sensors) limits the maximum levels of sound attenuation which can be achieved under ideal conditions. This paper presents a theoretical framework suitable for aiding in the design of feedforward active systems to c